Calculus in Several Variable
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Overview
Literature: Calculus: A Complete Course, Adams R. A. and Essex C., 9th ed, Pearson, 2018.
Module 1. 3-dimensional geometry and functions of several variables
Lecture 1
- 10.1 Analytic geometry in three dimensions
Exercises: 11, 25, 27, 29, 31, 33, 35, 37, 39
- 10.6 Cylindrical and spherical coordinates
Exercises: 3, 5, 9, 13
Lecture 2
- 11.1 Vector values functions in on variable
Exercises: 17, 21, 33
- 11.2 Applications of vector differentiation
Exercises: 3
- 11.3 Curves and parametrizations
Exercises: 5, 7, 11, 13, 15
Lecture 3
- 12.1 Functions in several variables
Exercises: 5, 9, 13,15, 17, 23, 27, 33
- 12.2 Limits and continuity
Exercises: 5, 7, 9, 11, 15
Module 2. Partial derivatives and linear approximation
Lecture 4
Exercises: 5, 7, 13, 23
- 12.4 Higher order derivatives
Exercises: 5, 7, 11, 15, 17
Exercises: 7, 11, 17, 21
Lecture 5
- 12.6 Linear approximation, differentiability and differentials
Exercises: 3, 5, 17, 19
- 12.7 Gradient and directional derivatives
Exercises: 3, 5, 13, 17, 25
Module 3. Applications of derivatives
Lecture 6
Exercises: 13, 17
- 12.9 Taylor's formula, Taylor series and approximation
Exercises: 1, 3, 5, 7, 11
Lecture 7
Exercises: 5, 7, 9, 19, 23, 25
- 13.2 Extreme values of functions with constraints
Exercises: 3, 5, 9, 15
�Lecture 8
- 13.3 Lagrange multipliers
Exercises: 3, 9, 11, 15
- 13.4 Lagrange multipliers in higher-dimensional spaces
Exercises: 1, 3
Module 4. Multiple integrals
Lecture 9
Exercises: 15, 19, 21
- 14.2 Iterated integration in cartesian coordinates
Exercises: 3, 5, 15, 23
Lecture 10
- 14.3 Generalized integrals and the mean value theorem
Exercises: 1, 3, 13, 27
- 14.4 Double integrals in polar coordinates
Exercises: 5, 9, 15, 19, 21
Lecture 11
Exercises: 5, 7, 9
- 14.6 Change of variables in triple integrals
Exercises: 3, 7, 11
- 14.7 Applications of multiple integrals
Exercises: 5, 9, 13, 21,27
Module 5. Line and surface integrals
Lecture 12
- 15.1 Vector fields and scalar fields
Exercises: 3, 5, 17
Exercises: 3, 5, 7, 21
Lecture 13
Exercises: 7, 11
- 15.4 Line integrals of vector fields
Exercises: 1, 5, 7, 15
Lecture 14
- 15.5 Surfaces and surface integrals
Exercises: 1, 7, 13
- 15.6 Oriented integrals and flux integrals
Exercises: 5, 9, 13, 15
Module 6. Vector Calculus
Lecture 15
- 16.1 Gradient, divergence and curl
Exercises: 3, 7, 11
- 16.2 Some identities involving grad, div and curl
Exercises: 9, 15, 17
Lecture 16
- 16.3 Green's Theorem in the plane
Exercises: 3, 5, 9
Lecture 17
- 16.4 The Divergence Theorem in three-dimensional space
Exercises: 5, 11, 15
- 16.5 Stoke's Theorem in three-dimensional space
Exercises: 1, 3, 5
Lecture 18