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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

12.3 Partial derivatives

Exercises: 5, 7, 13, 23

12.4 Higher order derivatives

Exercises: 5, 7, 11, 15, 17

12.5 The chain rule

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

12.8 Implicit functions

Exercises: 13, 17

12.9 Taylor's formula, Taylor series and approximation

Exercises: 1, 3, 5, 7, 11

Lecture 7

13.1 Extreme values

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

14.1 Double integrals

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

14.5 Tripple integrals

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

15.2 Conservative fields

Exercises: 3, 5, 7, 21

Lecture 13

15.3 Line integrals

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