Completed on December 7, 2017 with a grade of A.

• Note: Since I'm writing the textbook while studying, the notes and textbook are one.

## Syllabus

Based on the Stonybrook MAT 203: Calculus III with Applications Fall 2013
MAT 203 Syllabus[1]
MAT 203 Homework Solutions[2]
Description - Geometry for higher dimensional Euclidean space; vectors and vector functions; partial derivatives; multiple integrals; line integrals; vector fields; Green’s Theorem and Stoke’s Theorem.
Credits - 4 credits
Level - Bachelors (Upper Division)
Required Textbook: Calculus III Advanced Calculus, Chapters 11, 12, 13, 14, 15
Supplemental Textbook: Calculus 10th Edition, by Ron Larson and Bruce Edwards (Brooks/Cole Publ.)[3]
Exams

Exam Points
One exam per chapter 500
Final 300
Homework 200
-----
Total 1000

### Exams

Exam 1 - Chapter 11 - p. 811. 11, 20, 22, 30, 36, 39, 46, 50, 54, 60, 70. B
Exam 2 - Chapter 12 - p. 863. 11, 25, 29, 35, 41. A
Exam 3 - Chapter 13 - p. 960. 5, 15, 23, 33, 43, 47, 63, 69. A
Exam 4 - Chapter 14 - p. 1034. 3, 9, 13, 15, 17. A
Exam 5 - Chapter 15 - Skipped, go directly to the final exam.
Final Exam - Calculus III Advanced (Course) Final Exam A

### Homework Exercises

From Larson and Edward's Calculus 10th Edition[4]

• 11.1: 8, 28, 36, 50, 84
• 11.2: 6, 26, 44, 58, 84
• 11.3: 4, 10, 14, 42, 57, 62
• 11.4: 1-6, 10, 16, 28, 38
• 11.5: 10, 28, 29, 40, 42, 54, 82
• 11.6: 1-6, 10, 16, 32, 44
• 11.7: 4, 8, 26, 32, 38, 44
• 12.1: 2, 19-22, 24, 52, 68, 72
• 12.2: 4, 26, 42, 46, 52, 58
• 12.3: 18, 22, 26, 36
• 12.4: 10, 19, 22, 29-32
• 12.5: 10, 12, 17
• 13.1: 16, 24, 27, 38, 45-48, 52
• 13.2: 24, 74, 76
• 13.3: 18, 52, 60, 66, 78, 110
• 13.4: 14, 26, 30
• 13.5: 12, 16, 20, 21
• 13.6: 2, 24, 36, 52, 61
• 13.7: 10, 18, 24, 42
• 13.8: 6, 12, 18, 27-30, 42, 46
• 13.9: 6, 10, 14, 18
• 13.10: 6, 24, 34, 46
• 14.1: 28, 32, 42, 56, 60
• 14.2: 8, 12, 18, 24, 34, 48, 54
• 14.3: 6, 18, 22, 26, 30, 40, 44
• 14.4: 8, 23
• 14.5: 5, 7
• 14.6: 6, 14, 21, 26, 36, 38
• 14.7: 10, 12, 18, 36
• 14.8: 3, 11
• 15.1: 1, 2, 3, 4, 8, 34, 40, 44, 60
• 15.2: 6, 10, 20, 22, 30, 38, 54.

## Chapter 11 Vectors and Spacial Geometry

### 11.1 Vectors in Two Dimensions

Exercises 8, 28, 36, 50, 84
Calculus III Advanced (Course) (11.1) (Homework)

### 11.2 Coordinates and Vectors in Three Dimensions

Exercises 6, 26, 44, 58, 84
Calculus III Advanced (Course) (11.2) (Homework)

### 11.3 The Dot Product for Two Vectors in Three Dimensions

Exercises 4, 10 ,14, 42, 57, 62
Calculus III Advanced (Course) (11.3) (Homework)

### 11.4 The Cross Product for Two Vectors in Three Dimensions

Exercises 1, 2, 3, 4, 5, 6, 10, 16, 28, 38
Calculus III Advanced (Course) (11.4) (Homework)

### 11.5 Lines and Planes in Three Dimensions

Exercises 10, 28, 29, 40, 42, 54, 82
Calculus III Advanced (Course) (11.5) (Homework)

### 11.6 Surfaces in Three Dimensions

Exercises 1, 2, 3, 4, 5, 6, 10, 16, 32, 44
Calculus III Advanced (Course) (11.6) (Homework)

### 11.7 Cylindrical and Spherical Coordinates

Exercises 4, 8, 26, 32, 38, 44
Calculus III Advanced (Course) (11.7) (Homework)
A-

### Chapter 11 Exam

Exercises 11, 20, 22, 30, 36, 39, 46, 50, 54, 60, 70
B

## Chapter 12 Vector-Valued Functions

### 12.01 Vector-Valued Functions

Exercises 2, 19, 20, 21, 22, 24, 52, 68, 72
Calculus III Advanced (Course) (12.1) (Homework)
A

### 12.02 Differentiation and Integration for Vector-Valued Functions

Exercises 4, 26, 42, 46, 52, 58
Calculus III Advanced (Course) (12.2) (Homework)
A

### 12.03 Velocity and Acceleration

Exercises 18, 22, 26, 36
Calculus III Advanced (Course) (12.3) (Homework)
A

### 12.04 Tangent Vectors and Normal Vectors

Exercises 10, 19, 22, 29, 30, 31, 32
Calculus III Advanced (Course) (12.4) (Homework)
A

### 12.05 Arc Length and Curvature

Exercises 10, 12, 17
Calculus III Advanced (Course) (12.5) (Homework)
A

### Chapter 12 Exam

Exercises 11, 25, 29, 35, 41
A

## Chapter 13 Functions with Several Variables

### 13.01 Functions with Several Variables

Exercises 16, 24, 27, 38, 45, 46, 47, 48, 52
Calculus III Advanced (Course) (13.1) (Homework)
A

### 13.02 Limits and Continuity

Exercises 24, 74, 76
Calculus III Advanced (Course) (13.2) (Homework)
A

### 13.03 Partial Derivatives

Exercises 18, 52, 60, 66, 78, 110
Calculus III Advanced (Course) (13.3) (Homework)
A

### 13.04 Differentials

Exercises 14, 26, 30
Calculus III Advanced (Course) (13.4) (Homework)
A

### 13.05 Chain Rules for Functions with Several Variables

Exercises 12, 16, 20, 21
Calculus III Advanced (Course) (13.5) (Homework)
A

### 13.06 Directional Derivatives and Gradients

Exercises 2, 24, 36, 52, 61
Calculus III Advanced (Course) (13.6) (Homework)
A

### 13.07 Tangent Planes and Normal Lines

Exercises 10, 18, 24, 42
Calculus III Advanced (Course) (13.7) (Homework)
A

### 13.08 Extrema for Functions with Two Variables

Exercises 6, 12, 18, 27, 28, 29, 30, 42, 46
Calculus III Advanced (Course) (13.8) (Homework)
B

### 13.09 Extrema Applications

Calculus III Advanced (Course) (13.9) (Homework)
Exercises 6, 10, 14, 18.
B

### 13.10 Lagrange Multipliers

Calculus III Advanced (Course) (13.10) (Homework)
Exercises 6, 24, 34, 46.
B

### Chapter 13 Exam

Exercises 6, 15, 23, 33, 43, 47, 63, 69.
A

## Chapter 14 Multiple Integration

### 14.01 Iterated Integrals and Area in the Plane

Calculus III Advanced (Course) (14.01) (Homework)
Exercises 28, 32, 42, 56, 60.
A

### 14.02 Double Integrals and Volume

Calculus III Advanced (Course) (14.02) (Homework)
Exercises 8, 12, 18, 24, 34, 48, 54
B

### 14.03 Double Integrals in Polar Coordinates

Calculus III Advanced (Course) (14.03) (Homework)
Exercises 6, 18, 22, 26, 30, 40, 44
B

### 14.04 Mass Center and Inertia Moments

Calculus III Advanced (Course) (14.04) (Homework)
Exercises 8, 33
A

### 14.05 Surface Area

Calculus III Advanced (Course) (14.05) (Homework)
Exercises 5, 7
A

### 14.06 Triple Integrals and Applications

Calculus III Advanced (Course) (14.06) (Homework)
Exercises 6, 14, 21, 26, 36, 38
A

### 14.07 Triple Integrals in Other Coordinates

Calculus III Advanced (Course) (14.07) (Homework)
Exercises 26, 36
A

### 14.08 Jacobian Variables

Calculus III Advanced (Course) (14.08) (Homework)
Exercises 3, 11
A

### Chapter 14 Exam

Exercises 3, 9, 13, 15, 17.
A

## Chapter 15 Vector Analysis

### 15.01 Vector Fields

Calculus III Advanced (Course) (15.01) (Homework)
Exercises 1, 2, 3, 4, 8, 34, 40, 44, 60
A

### 15.02 Line Integrals

Calculus III Advanced (Course) (15.02) (Homework)
Exercises 6, 10, 20, 22, 30, 38, 54
C

### 15.03 Conservative Vector Fields and Independent Path

Calculus III Advanced (Course) (15.03) (Homework)
Exercises 1, 16, 26, 36
C