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General Course Description
The course explores vectors, multidimensional integrals and their applications, integral theorems, coordinate transformations, and suffix notation for compactly writing vector equations and proving vector identities.
Textbook (Not Required)
James Stewart, Calculus (early or late transcendentals), any edition, Cengage Learning
Harry F. Davis & Arthur Snider, Introduction to Vector Analysis, 7th Edition, 2000, Hawkes Publishing
Earlier editions may work for reference as well.
Paul C. Matthews, Vector Calculus, Springer Undergraduate Mathematics Series, 1998, Springer-Verlag London
Murray R. Spiegel, Schaum's Outline: Vector Analysis and an Introduction to Tensor Analysis, 1959, McGraw-Hill, Inc.
Course Material - Document:
A Primer on Index Notation by John Crimaldi
This is not as comprehensive as what will be covered in class. However, it also touches on a couple of things we may not cover thoroughly. Hopefully, the PDF file will be helpful to any student seeking additional resources.
Homework
Homework problems come from a combination of the recommended textbooks.
Exams
Midterm Exam #1: Homework 1 - 3
Vectors
Dot Product
Cross Product
Integrals
Line Integrals: length, mass, center of mass (c.o.m.), moment of inertia (m.o.i.), work
Surface Integrals: area, mass, c.o.m., m.o.i., flux
Volume Integrals: volume, mass, c.o.m., m.o.i.
Midterm Exam #2: Homework 4 - 7
Integral Theorems: Green's Theorem, Stokes' Theorem, and the Divergence Theorem
Suffix Notation: Scalars, Vectors, and Tensors
Kronecker Delta & Alternating Tensor (Levi-Civita)
Final Exam (Cumulative): Homework 1-8
In addition to all of the above topics, the final exam will cover the topic of Change of Variables.
*There will be an in-class review session prior to every exam.
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