Mathematical Methods for Economists HT26

Section outline

• Select section Mathematical Methods for Economists

  Collapse Expand

  Mathematical Methods for Economists

  Collapse all Expand all

  Teaching

  Instructor:  Sofia Tirabassi tirabassi@math.su.se

  Teaching assistant: Edoardo Mason edoardo.mason@math.su.se

  Course literature: Sydsaeter, K & Hammond, P., Essential Mathematics for Economic Analysis (7:th ed., Pearson 2026) ISBN 978-1-292-75575-5.

  Pearson offer students 20% discount on the digital version (and 25% for student union members, SUS and FEST). All information is on the attached pdf. 

   

  Below is also the direct link and the discount code which is valid for all Pearson digital titles until June 30^th 2027.

   

  Essential Mathematics for Economic Analysis

   

  Discount code SUDISCOUNT2627

   

  There is a Pdf here with al the information.

  !!! The new edition changed almost nothing of what we covered, if you have an old edition from a friends or so, you can still make do. Just be aware that the page number is off.

  Some additional videos will be available, but should not be seen as substitutions for the live lectures.

   

  
  Schedule:  The first class is 13:00-15:00 Monday 2026-09-03. NO TA SESSION ON THE FIRST DAY 
                     After that:
                     Lectures Mondays and Thursdays 13:00-15:00 and TA Sessions 5 15:00-17:00 (Starting from 2025-01-23)
  
  This is a day time on campus course and the lectures are on campus.

  Examination

  Examiner: Sofia Tirabassi
  
  Grading criteria The grade is determined by the final exam.

  
  There will be three sets of homework. The homework will not give you a bonus point but they are useful to stay in pace with the lectures. One of the exercises in the second or third set of homework will be given in the written exam. 

   1. The first homework  is more of a self test, if you struggle you should go back and review your high school math.

  2. The second and third homework will consist of exercises very similar to those that you will get in the final exam. One  exercise or part of one exrcise worth between 3 and 5 points will appear verbatim in the final exam. No solution will be given to the homework, but if you submit them on time you will get corrections.

  A .pdf with the text of the homework will be made available here on the course web page.
  
  

  Final exam:  October 26th, 2026. 14:00-19:00  You will be provided a calculator for the test, the Casio FX-82 Solar II.

  Final exam retake: TBA You will be provided a calculator for the test, the Casio FX-82 Solar II.

  
  Remember to register for the finals in LADOK.

  Examination Rules at the Department of Mathematics.

  
  
  

  • Select activity Previous finals

    

    Previous finals URL
  • Select activity News forum

    

    News forum
  • Select activity Discussion forum

    

    Discussion forum

    Here you can post theory question. We will answer asap

  • Select activity Q&A

    

    Q&A Forum

    If you have specific questions on exercises please ask them here so that everyone can enjoy and learn from our answers!

    Please title the question with the exercise number or with a title which helps the reader understanding what this is about, so that your colleague will navigate the forum easily.

    You can also answer your own questions or question posed by other.

  • Select activity Kursplan

    

    Kursplan File
  • Select activity Betygskriterier

    

    Betygskriterier Page
  • Select activity Exam Formula Sheet-updated

    

    Exam Formula Sheet-updated File
  • Select activity User manual Calculator FX-82 Solar

    

    User manual Calculator FX-82 Solar File
  • Select activity Extended formula sheet (not available for the final)

    

    Extended formula sheet (not available for the final) File
  • Select activity Segnalation Misprints in Old Exams

    

    Segnalation Misprints in Old Exams Forum
  • Select activity Discount on textbook

    

    Discount on textbook File
• Select section Prologue

  Collapse Expand

  Prologue

  
  

  • Select activity A nice website

    

    A nice website URL

    This is a website created by the Economics Department of the University of Warwik. Its goal is to help students refresh A-level (high school advanced) math in order to be successful in their economic degrees. It cover many topics in our syllabus, you can find extra material and extra exercises,  everything made by economists. In addition, there are many motivational videos, create by economists, which underline the importance of math in Economics.

• Select section Dag 1 : Elementary algebra

  Collapse Expand

  Dag 1 : Elementary algebra

  Repetition on elementary algebra (2.1-2.5)

  Suggested exercises:

  2.2: 1, 4, 8, 13, 14 pp. 31-32

  2.3: 1, 3, 5, 11 pp. 36-37

  2.4: 1, 2, 3, 4, 6 p. 41-42

  2.5: 1, 2, 4, 8, 10, 13 p. 46-47

  2.11: 1

  (the section 2 from the 6th and 5th edition  is section 1 in the 4th. If you have the 4th edition, replace 2.# with 1.# and don't rely on the above page indications). The pages of the exercises refers to the 6th edition, which are different from earlier editions.

  • Select activity 2-Powers.mp4 (Lang)

    2-Powers.mp4 (Lang)
  • Select activity 1-Real_Numbers.mp4 (Lang)

    1-Real_Numbers.mp4 (Lang)
  • Select activity 3-Algebraic_operationssimplifications.mp4

    3-Algebraic_operationssimplifications.mp4
  • Select activity 4-Binomial_coefficients.mp4 (Lang)

    4-Binomial_coefficients.mp4 (Lang)
  • Select activity Self Test

    

    Self Test File

    Try and see how much you remember from your Matte 3. We are going to re-cover some of these topic, so do not panic if this seems impossible. But...  it is good to be aware of a problem before it get out of control.
  • Select activity Solution to slides

    

    Solution to slides File
  • Select activity Slides Lecture 1

    

    Slides Lecture 1 File
• Select section Dag 2: Linear and quadratic functions

  Collapse Expand

  Dag 2: Linear and quadratic functions

  Intervals, absolute values (2.7)

  Graphs, linear and quadratic functions (4.1-4.6)

  Suggested exercises:

  2.7: 2, 3 a-d p. 55

  4.2: 3, 6, 10 pp. 103-104,

  4.4: 5, 6, 7 p. 113,

  4.5: 3 p. 117

  4.6:  2, 3 p. 123-124

  • Select activity 1-Set_theory.mp4

    1-Set_theory.mp4
  • Select activity 2-Intervals_absoluteValues.mp4

    2-Intervals_absoluteValues.mp4
  • Select activity 3-FunctionsGraphs.mp4

    3-FunctionsGraphs.mp4
  • Select activity 4-LinearFunctions.mp4

    4-LinearFunctions.mp4
  • Select activity 5-QuadraticFunctions.mp4

    5-QuadraticFunctions.mp4
  • Select activity Solution to Slides Lecture 2

    

    Solution to Slides Lecture 2 File
  • Select activity Slides for Lecture 2

    

    Slides for Lecture 2 File
• Select section Dag 3: Other functions

  Collapse Expand

  Dag 3: Other functions

  Polynomials, power functions, exponential, logarithm (4.7-4.10)  

  Suggested exercises:

  4.7:  2, 4 p. 132

  4.8: 1, 3 p.134

  4.9: 1, 2, 4, 5, 6 p. 138-139

  4.10: 1, 2, 5, 7 p. 144-145

  • Select activity 1-Polynomials.mp4 (Lang)

    1-Polynomials.mp4 (Lang)
  • Select activity 2-PowerFunctions.mp4 (Lang)

    2-PowerFunctions.mp4 (Lang)
  • Select activity 3-Exponential_Logarithm.mp4 (Lang)

    3-Exponential_Logarithm.mp4 (Lang)
  • Select activity Long Division of Polynomials

    

    Long Division of Polynomials File
  • Select activity Worksheet

    

    Worksheet File
  • Select activity Video Long Polynomial Division

    

    Video Long Polynomial Division URL
  • Select activity Graphs of some basic functions

    

    Graphs of some basic functions File
  • Select activity Solution to slides lecture 3

    

    Solution to slides lecture 3 File
  • Select activity Lecture 3 Slides

    

    Lecture 3 Slides File
• Select section Dag 4: Geometric Sum and Series

  Collapse Expand

  Dag 4: Geometric Sum and Series

  
  

  §11.4 Geometric Series 
  

  §11.5 Total present value

  §11.6 Mortage repaiments

  Attention: Chapter 10, 11, and 14 in the sixth edition were chapter 9, 10 and 11 in the 5th.

  
  

  Exercises:

  §11.4: 2, 3, 4, 5 p. 413

  §11.5: 1, 2, 3, 4, 5 p. 418-419

  §11.4: 1, 2, 3 p 423

  
  

  
  

  • Select activity Solution to slides lecture 4

    

    Solution to slides lecture 4 File
  • Select activity Lecture 4 slides

    

    Lecture 4 slides File
• Select section Dag 5: Derivatives I

  Collapse Expand

  Dag 5: Derivatives I

  About derivatives #1 (6.1-6.8, 6.10-6.11)

  Suggested exercises:

  6.1: 1, 2 pp. 180-181

  6.2: 1, 4, 5, 6, 7, 8 p. 186

  6.5: 1, 4, 5, 6 pp. 198-199,

  6.6: 1-4 pp. 202-203, 

  6.7: 2, 3, 7, 8 pp. 209-210

  6.8: 2, 3a,c, 6, 12 p. 215-216

  6.10: 1, 2a-b, 6a-b p. 221-222

  6.11: 2a,c, 3b-c,e-h p. 227

  • Select activity 1-Slopes_Tangents_Derivative.mp4

    1-Slopes_Tangents_Derivative.mp4
  • Select activity 2-IncreasingDecreasingFunctions.mp4

    2-IncreasingDecreasingFunctions.mp4
  • Select activity 3-Limits.mp4

    3-Limits.mp4
  • Select activity 4-RulesDerivative.mp4

    4-RulesDerivative.mp4
  • Select activity Solutions To Lecture 5 Slides

    

    Solutions To Lecture 5 Slides File

    Available from 15 September 2026, 9:00 AM
  • Select activity Lecture 5 Slides

    

    Lecture 5 Slides File
• Select section Dag 6 Implicit Derivation

  Collapse Expand

  Dag 6 Implicit Derivation

  §7.1: Implicit derivation

  §7.4-7.5 Linear and polynomial approximations 

  §7.6 Taylor's formula

  Exercises

  §7.1: 1, 2, 3, 7a, 8 p. 236

  §7.4: 2, 3, 4, 6 p. 249

  §7.5: 1, 2, 3, 5 p. 253

  §7.6: 1, 3, 4 p 257

  • Select activity 7*4-LinearApproximation.mp4

    7*4-LinearApproximation.mp4
  • Select activity 7*5-PolynomialApproximation.mp4

    7*5-PolynomialApproximation.mp4
  • Select activity 7*6-TaylorFormula.mp4

    7*6-TaylorFormula.mp4
  • Select activity 7*8-Continuity.mp4

    7*8-Continuity.mp4
  • Select activity 7*9-Limits(2).mp4

    7*9-Limits(2).mp4
  • Select activity Solution to slides- implicit derivation

    

    Solution to slides- implicit derivation File
  • Select activity Solution to slides -Taylor polynomial and taylor formula

    

    Solution to slides -Taylor polynomial and taylor formula File
  • Select activity Worked out examples for implicit derivations and Taylor polynomials

    

    Worked out examples for implicit derivations and Taylor polynomials URL

    Some worked out examples that I did not manage to do  during the lecture PGA fire alarm...

  • Select activity Use of Taylor Series in Finance

    

    Use of Taylor Series in Finance URL
  • Select activity Article (written by economist) in which Taylor series are used

    

    Article (written by economist) in which Taylor series are used File
  • Select activity Article II with applications of degree 2 Taylor polynomials

    

    Article II with applications of degree 2 Taylor polynomials File
  • Select activity Slide for lecture 5

    

    Slide for lecture 5 File
• Select section Dag 7: Conitinuity and Limits

  Collapse Expand

  Dag 7: Conitinuity and Limits

  7.8 Continuity 

  7.9 More on limits 

  7.12 L'Hopital's rule

  10.1 Indefinite Integrals

  Exercises:

  7.8: 2, 3 p. 267

  7.9: 1, 2 p. 275-277

  7.12: 1 a, b p. 289

  10.1  1 a-c e-g, 2, 3, 4, 11, 12 p. 360-361

  • Select activity Slides for Lecture 6

    

    Slides for Lecture 6 File
  • Select activity Limits of elementary functions (to now)

    

    Limits of elementary functions (to now) File
  • Select activity 1-RulesDerivative.mp4

    1-RulesDerivative.mp4
  • Select activity 2-Exponential(2).mp4

    2-Exponential(2).mp4
  • Select activity 3-Logarithm(2).mp4

    3-Logarithm(2).mp4
  • Select activity 4-ImplicitDifferentiation.mp4

    4-ImplicitDifferentiation.mp4
  • Select activity Solution to slides 7

    

    Solution to slides 7 File
  • Select activity Homework 1

    

    Homework 1 Assignment
  • Select activity Lecture 7 Slides

    

    Lecture 7 Slides File
• Select section Dag 8: Optimization in 1 variable

  Collapse Expand

  Dag 8: Optimization in 1 variable

  §9.1 Extreme points 

  §9.2 Simple Tests for Extreme Points 

  §9.4 The Extreme Value Theorem 

  §9.6 Local Extreme Points

  §8.6 Inflection Points 

  Attention: Here the 6th and 5th edition of the book start to differ a lot. Section 9.1-9.6 of the sixth editions are 8.1-8.6 in the 5th. Section 8.6 in the 6th editions is section 8.7 in the fifth.

  
  

  Exercises

  §9.1: 1 p. 324
  

  §9.2: 1, 2, 5, 7 p. 327-328
  

  §9.4: 1, 2 p. 339
  

  §9.6: 1, 3, 5, 6 p. 351

  §8.6: 1, 2, 3 p.319

  
  
  

  • Select activity 8*1-ExtremePoints.mp4

    8*1-ExtremePoints.mp4
  • Select activity 8*4-ExtremeValueTheorem.mp4

    8*4-ExtremeValueTheorem.mp4
  • Select activity 8*7-InflectionPoints.mp4

    8*7-InflectionPoints.mp4
  • Select activity Solution to slide exercises

    

    Solution to slide exercises File
  • Select activity Solution to slide example 8

    

    Solution to slide example 8 File
  • Select activity Slide for lecture 8

    

    Slide for lecture 8 File
• Select section Dag 9: Integrals

  Collapse Expand

  Dag 9: Integrals

  §10.2 Area and Definite Integrals 

  §10.3 Properties of Definite Integrals

  §10.5 Integration by Parts 

  §10.6 Integration by Substitution 

  §10.7 Infinite Intervals of Integration 

  Attention: Chapter 10 in the 6th edition is chapter 9 in the 5th.

  Exercises

  §10.2: 2, 5, 7, 8 p. 369

  §10.3:  9a-c, 10 p. 373

  §10.5:  1-3, 10 p. 384

  §10.6: 1, 2, 3, 4 p. 389

  §10.7: 1 p. 395

  • Select activity 9*1-IndefiniteIntegrals.mp4

    9*1-IndefiniteIntegrals.mp4
  • Select activity 9*2-AreaDefiniteIntegrals.mp4

    9*2-AreaDefiniteIntegrals.mp4
  • Select activity 9*3-PropertiesIntegrals.mp4

    9*3-PropertiesIntegrals.mp4
  • Select activity Solution to slide examples integrals

    

    Solution to slide examples integrals File
  • Select activity Slides for lecture 9

    

    Slides for lecture 9 File
• Select section Dag 10: Partial Derivatives

  Collapse Expand

  Dag 10: Partial Derivatives

  §14.1 Functions of Two Variables 

  §14.2 Partial Derivatives with Two Variables

  §14.3 Geometric Representation
  
  

  §14.4 Surfaces and Distance

  Attention: Chapter 14 in the sixth edition was 11 in the fifth.

  Exercises

  §14.1: 1, 3, 4, 6, 7 p. 566-567

  §14.2: 2, 3, 4, 5, 7 p. 573

  §14.4: 2, 3 4 p. 583

  • Select activity Slide for lectures 10 and 11

    

    Slide for lectures 10 and 11 File
  • Select activity 11*3-GeometricRepresentations.mp4

    11*3-GeometricRepresentations.mp4
  • Select activity 11*4-SurfacesAndDistance.mp4

    11*4-SurfacesAndDistance.mp4
  • Select activity 11*56-FunctionsOfMoreVariables.mp4

    11*56-FunctionsOfMoreVariables.mp4
  • Select activity 11*7-EconomicApplications.mp4

    11*7-EconomicApplications.mp4
  • Select activity Solution to slides 10/11

    

    Solution to slides 10/11 File
  • Select activity Lecture 10 Slides

    

    Lecture 10 Slides File
• Select section Dag 11: Optimization in 2 variables, the interior.

  Collapse Expand

  Dag 11: Optimization in 2 variables, the interior.

  §15.1 A simple chain rule

  §17.1 Two Variables: Necessary Conditions 

  §17.2 Two Variables: Sufficient Conditions 

  §17.3 Unconstrained optimization 

  Attention: Chapters 15 and 17 in the 6th edition were chapter 12 and 13 in the 5th.

  Exercises:

  §15.1: 1, 2, 3 p. 620

  §17.1: 1,2, 4 p. 716

  §17.2: 4, 5 p. 721

  §17.3 : 1, 2 p. 726

  • Select activity 12*1-SimpleChainRule.mp4

    12*1-SimpleChainRule.mp4
  • Select activity 13*1-ExtremaNecessaryC.mp4

    13*1-ExtremaNecessaryC.mp4
  • Select activity 13*2-ExtremaSufficientC.mp4

    13*2-ExtremaSufficientC.mp4
  • Select activity Lecture 11 Slides

    

    Lecture 11 Slides File
• Select section Dag 12 : Optimization in 2 variables, the boundary

  Collapse Expand

  Dag 12 : Optimization in 2 variables, the boundary

  §17.5 The Extreme Value Theorem

  §18.1 The Lagrange Multiplier Method 

  Attention: Ch 17 and 18 in the 6th edition  were 13 and 14 respectively in the 5th.

  Exercises

  §17.5: 2, 3, 4 p. 738

  §18.1: 4, 5 p. 760

  • Select activity 13*3-LocalExtremePoints.mp4

    13*3-LocalExtremePoints.mp4
  • Select activity 13*5-ExtremeValueTheorem.mp4

    13*5-ExtremeValueTheorem.mp4
  • Select activity 14*1-LagrangeMultipliers.mp4

    14*1-LagrangeMultipliers.mp4
  • Select activity 15*1-SystemsOfLinearEquations.mp4

    15*1-SystemsOfLinearEquations.mp4
  • Select activity 15*2-Matrices.mp4

    15*2-Matrices.mp4
  • Select activity Lecture 12 Slides

    

    Lecture 12 Slides File
• Select section Dag 13: Gauss-Jordan elimination

  Collapse Expand

  Dag 13: Gauss-Jordan elimination

  Matrices and Linear Systems

  §12.1 Matrices and Vectors

  §12.2 System of linear equations

  §12.3 Matrix Addition

  §12.4 Algebra of Vectors

  §12.5 Matrix Multiplication
  

  §12.6 Rules for Matrix Multiplication

  §12.7 The Transpose

  §12.8 Gaussian Elimination

  Attention: In the 5th edition this material was explained in chapter 15.

  Exercise

  §12.1: 2, 3 p. 450

  §12.2: 1,  3, 4 p. 452

  §12.3: 1,  2  p. 454

  §12.4: 1, 3 p. 457

  §12.5: 1, 3, 4 p. 462

  §12.7: 1,2 p. 473

  §12.8: 1, 2, 3, 4 p. 479-480

  
  
  

  • Select activity 15*3-MatrixMultiplication.mp4

    15*3-MatrixMultiplication.mp4
  • Select activity 15*4-RulesMatrixMultiplication.mp4

    15*4-RulesMatrixMultiplication.mp4
  • Select activity 15*5-Transpose.mp4

    15*5-Transpose.mp4
  • Select activity 15*6-GaussianElimination.mp4

    15*6-GaussianElimination.mp4
  • Select activity Solutions to slides 13

    

    Solutions to slides 13 File
  • Select activity Lecture 13 Slides

    

    Lecture 13 Slides File
• Select section Dag 14 : Determinant and solution to linear systems

  Collapse Expand

  Dag 14 : Determinant and solution to linear systems

  Attention: Remember to enroll in the exam!

   

  §13.1 Determinants of Order 2

  §13.2 Determinants of Order 3

  §13.4 Basic Rules for Determinants

  §13.6 The Inverse of a Matrix

  Attention:  Chapter 13 in the 6th edition was 16 in the fifth

  
  
  

  Exercises

  §13.1: 1, 2, 5 p. 498-499

  §13.2: 1, 2, 3, 4 , 6 p. 503-504

  §13.4: 2, 8 p. 512-513

  §13.6: 1, 3 p. 523

  • Select activity Homework Assignement

    

    Homework Assignement Assignment
  • Select activity 16*1-Determinant2.mp4

    16*1-Determinant2.mp4
  • Select activity 16*24-Determinant3Rules.mp4

    16*24-Determinant3Rules.mp4
  • Select activity 16*6-Inverse.mp4

    16*6-Inverse.mp4
  • Select activity Solution to slides 14

    

    Solution to slides 14 File
  • Select activity Lecture 14 Slides

    

    Lecture 14 Slides File
• Select section Dag 15

  Collapse Expand

  Dag 15

  Repetition

  
  

  
  

  
  

  Note on calculators:  these will be given to you by the proctoring staff on finals day!

  Good luck on the final!
  

  
  

  
  

  • Select activity Solution hW 3

    

    Solution hW 3 File

    Available from 24 October 2026, 10:00 AM
• Select section New section

  Collapse Expand

  New section
• Select section Solutions to Exams

  Collapse Expand

  Solutions to Exams

  • Select activity Solution to Exam 20240313

    

    Solution to Exam 20240313 File
  • Select activity Solution to the exam

    

    Solution to the exam File
• Select section Video-länkar

  Collapse Expand

  Video-länkar

  Not available
• Select section Topic 20

  Collapse Expand

  Topic 20

  We reserve the rights to update, change, replace or modify parts of the course contents (while adhering to the course description). Such changes will be communicated via the course webpage, or during the lectures. It is the responsibility of the student to stay updated with such changes.