Calculus III Advanced (Course)
Completed on December 7, 2017 with a grade of A.
Contents
- 1 Calculus III Advanced (Course)
- 1.1 Syllabus
- 1.2 Chapter 11 Vectors and Spacial Geometry
- 1.2.1 11.1 Vectors in Two Dimensions
- 1.2.2 11.2 Coordinates and Vectors in Three Dimensions
- 1.2.3 11.3 The Dot Product for Two Vectors in Three Dimensions
- 1.2.4 11.4 The Cross Product for Two Vectors in Three Dimensions
- 1.2.5 11.5 Lines and Planes in Three Dimensions
- 1.2.6 11.6 Surfaces in Three Dimensions
- 1.2.7 11.7 Cylindrical and Spherical Coordinates
- 1.2.8 Chapter 11 Exam
- 1.3 Chapter 12 Vector-Valued Functions
- 1.4 Chapter 13 Functions with Several Variables
- 1.4.1 13.01 Functions with Several Variables
- 1.4.2 13.02 Limits and Continuity
- 1.4.3 13.03 Partial Derivatives
- 1.4.4 13.04 Differentials
- 1.4.5 13.05 Chain Rules for Functions with Several Variables
- 1.4.6 13.06 Directional Derivatives and Gradients
- 1.4.7 13.07 Tangent Planes and Normal Lines
- 1.4.8 13.08 Extrema for Functions with Two Variables
- 1.4.9 13.09 Extrema Applications
- 1.4.10 13.10 Lagrange Multipliers
- 1.4.11 Chapter 13 Exam
- 1.5 Chapter 14 Multiple Integration
- 1.5.1 14.01 Iterated Integrals and Area in the Plane
- 1.5.2 14.02 Double Integrals and Volume
- 1.5.3 14.03 Double Integrals in Polar Coordinates
- 1.5.4 14.04 Mass Center and Inertia Moments
- 1.5.5 14.05 Surface Area
- 1.5.6 14.06 Triple Integrals and Applications
- 1.5.7 14.07 Triple Integrals in Other Coordinates
- 1.5.8 14.08 Jacobian Variables
- 1.5.9 Chapter 14 Exam
- 1.6 Chapter 15 Vector Analysis
- 2 Internal Links
Calculus III Advanced (Course)
- 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)
Passing Grade - "C", 2.0
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.
Calculus III Advanced (Course)(Notes)
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)
Grade A
11.2 Coordinates and Vectors in Three Dimensions
Exercises 6, 26, 44, 58, 84
Calculus III Advanced (Course) (11.2) (Homework)
Grade A
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)
Grade A
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)
Grade A
11.5 Lines and Planes in Three Dimensions
Exercises 10, 28, 29, 40, 42, 54, 82
Calculus III Advanced (Course) (11.5) (Homework)
Grade A
11.6 Surfaces in Three Dimensions
Exercises 1, 2, 3, 4, 5, 6, 10, 16, 32, 44
Calculus III Advanced (Course) (11.6) (Homework)
Grade A-
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
15.04 Green's Theorem
15.05 Parametric Surfaces
15.06 Surface Integrals
15.07 Divergence Theorem
15.08 Stokes's Theorem
Internal Links
Parent Article: Matriculation