Advanced Calculus with Physical Applications

 

A course to follow differential and integral calculus

 

Independent study contract

 

Week

Topic(s)

Quiz

 

Problem set

Problem set

1

Parametric equations and curves

09/03-09/13

Notes

Questions

Answers

2

Polar coordinates

09/09-09/13

Notes

Questions

Answers

3

Conic sections

09/16-09/20

Notes

Questions

Answers

4

3D coordinate systems, vectors

09/23-09/27

Notes

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Answers

5

Dot product and cross product

10/01-10/04

Notes

Questions

Answers

6

Equations of lines and planes

10/07-10/11

Notes

Questions

Answers

7

Equations of cylinders and quadratic surfaces

10/16-10/18

Notes

Questions

Answers

8

Vector functions and their derivatives

10/21-10/25

Notes

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Answers

9

Arc length and curvature, motion in space

10/28-11/01

Notes

Questions

Answers

10

Functions of several variables

11/04-11/08

Notes

Questions

Answers

11

Partial derivatives

11/12-11/15

Notes

Questions

Answers

12

Tangent planes and linear approximations

11/18-11/22

Notes

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Answers

13

The chain rule

12/02-12/06

Notes

Questions

Answers

14

Directional derivatives and the gradient vector

12/09-12/13

Notes

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Answers

15

Minimum and maximum values, Lagrange multipliers

12/16-12/20

Notes

Questions

Answers

16

Introduction to double integrals and iterated integrals

01/02-01/03

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Answers

17

Double integrals

01/06-01/10

Notes

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Answers

18

Applications of double integrals and surface area

01/13-01/16

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Answers

19

Triple integrals

01/21-01/24

Notes

Questions

Answers

20

Vector fields

01/27-01/31

Notes

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Answers

21

Line integrals

02/03-02/07

Notes

Questions

Answers

22

Greenís theorem

02/10-02/14

Notes

Questions

Answers

23

Curl and divergence

02/24-02/28

Notes

Questions

Answers

24

Parametric surfaces

03/02-03/06

Notes

Questions

Answers

25

Surface integrals

03/09-03/12

Notes

Questions

Answers

26

Stokesí theorem

03/16-03/20

Notes

Questions

Answers

27

Divergence theorem

03/23-03/27

Notes

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Answers

28

Gaussís laws

03/30-04/03

Notes

Questions

Answers

29

Faradayís law

04/06-04/09

Notes

Questions

Answers

30

Ampere-Maxwell law

04/13-04/17

Notes

Questions

Answers

31

The speed of light

04/27-05/01

Notes

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Answers

32

First-order linear differential equations

05/04-05/08

Notes

Questions

Answers

33

Applications

05/11-05/15

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Answers

34

Second-order linear differential equations

05/18-05/22

Notes

Questions

Answers

35

Applications

05/26-05/29

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Questions

Answers