Ämnesdisposition
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MM1005 HT21, 7.5 hp
Teaching
Instructors
Salvador Rodriguez-Lopez,s.rodriguez-lopez@math.su.se
Dario Giandinoto, dario.giandinoto@math.su.se
Please include “MM1005”, without the quotes, in the subject line of course-related emails.
Course literature
Textbook: Essential Mathematics for Economic Analysis, Sydsæter & Hammond, 6th ed., Pearson
Note if using a different edition of the book: most content is the same, but page/section/exercise numbering may be different. All references in course material will use the 6th edition numbering.
Schedule
Exact time and room vary; see full schedule for details.
NOTE on 5/9 we will have 4 hours lecures, and on 9/9 the 4 hours will be dedicated to Tutorial session.
To register previously in Ladok is obligatory to be able to sit the exam, at least 15 working days previous to the exam date.
Syllabus
Detailed syllabus and lecture plan. Official course plan: Swedish, English
Examination
Examination
The course grade is based on final examination only. The exam is on 30/9 (v40). The Re-exam (omtentamen) is on Tuesday 06/11 (v45).
Examiner: Salvador Rodriguez-Lopez
Grading criteria: See syllabus
Examination Rules at the Department of Mathematics.
Resources
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General introduction + background
4.4 Linear Functions
4.6 Quadratic Functions4.7 PolynomialsSuggested exercises§4.4: 5, 6, 7 p. 115
§4.5: 3 p. 119
§4.6: 3, 5, 7 p. 126 -
4.7 Polynomials
4.8 Power Functions
4.9 Exponential Functions
4.10 Logarithmic Functions
§4.7: 2, 3, 4 p. 134§4.9:1, 2, 4, 5, 6 p. 140-141
§4.10: 1, 2, 5, 7 p. 146-147 -
6.1 Slopes of Curves
6.2 Tangents and Derivatives
6.3 Increasing and Decreasing Functions
6.5 A brief introduction to Limits
6.6 Simple Rules for Differentiation
6.7 Sums, Products, and Quotients§6.1 1, 2 p p. 182-183
§6.2: 1, 4, 5, 6, 7, 8 p. 188§6.5:1, 4, 5, 6 p p. 200-201
§6.6: 1-4 p p. 204-205,§6.7: 2, 3, 7, 8 p p. 211-212 -
6.8 Chain Rule
6.9 Higher-Order Derivatives6.10 Exponential Functions
6.11 Logarithmic Functions
7.1 Implicit Differentiation
7.4 Linear Approximations§6.8: 2, 3a,c, 6, 12 p. 217-218§6.9: 2, 4, 5 p. 219§6.10: 1, 2a-b, 6a-b p. 223-224
§6.11 2a,c, 3b-c,e-h p. 229
§7.1: 1, 2, 3, 7a, 8§7.4: 2-6 p. 251-252 -
7.5 Polynomial Approximation
7.6 Taylor’s Formula
§7.5: 1, 2, 3, 5 p. 255-256
§7.6: 1, 3, 4 p 259
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7.8 Continuity
7.9 More on Limits§7.8:2, 3 p. 269-270
§7.9: 1, 2 p. 277-278
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7.12 L’Hôpital’s Rule
7.10 Intermediate Value Theorem. Newton’s Method (*) Not covered in the notes (yet)
9.1 Extreme Points
9.2 Simple Tests for Extreme Points9.4 The Extreme Value Theorem9.6 Local Extreme Points§7.10: 1,4 p. 283
§7.12: 1, 2, 3 p. 29
§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 -
10.1 Indefinite Integrals
10.2 Area and Definite Integrals
10.3 Properties of Definite Integrals
10.5 Integration by Parts10.6 Integration by Substitution
10.7 Improper integrals§10.1: 1a-c,e-g, 2, 3, 4, 11, 12 p. 361
§10.2: 2, 5, 7, 8 p. 368
§10.3: 9a-c, 10 p. 372
§10.4: 2 p. 379§10.6: 1, 2, 3, 4 p. 388-389
§10.7: 1 p. 395 -
14.1 Functions of Two Variables
14.2 Partial Derivatives (Two Variables)14.3 Geometric Representation
14.4 Surfaces and Distance
14.5 Functions of More Variables
14.9 Economic applications
15.1 A Simple Chain Rule17.1 Two Variables: Necessary Conditions
§14.1: 1, 3, 4, 6, 7 p. 564-565
§14.2: 2, 3, 4, 5, 7 p. 571
§14.4: 2, 3 4 p. 580
§14.5: 1 p. 585
§14.9: 2 p. 607
§15.1: 1, 2, 3 p. 618§17.1: 1,2, 4 p. 694
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17.2 Two Variables: Sufficient Conditions
17.3 Local Extreme Points
17.5 The Extreme Value Theorem
18.1 The Lagrange Multiplier Method
§17.1: 1,2, 4 p. 694
§17.2: 4, 5 p. 699
§17.5: 2, 3, 4 p. 716
§18.1: 4, 5 p. 738 -
11.4 Geometric Series
11.5 Total present value
11.6 Mortage repaiments
11.4: 2, 3, 4, 5 p. 41311.5: 1, 2, 3, 4, 5 p. 418-419
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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
§18.1: 4, 5 p. 738
§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. 472
§12.8: 1, 2, 3, 4 p. 478-479 -
12.8 Gaussian Elimination
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
§16.1: 1, 2, 5 p. 498
§16.2: 1, 2, 3, 4 , 6 p. 504
§16.4: 2, 8 p. 513
§16.6: 1, 3 p. 523 -
12.2 System of linear equations
12.8 Gaussian Elimination
Relevant Exercises from previous years exams