# MAT 403 Calendar Spring 2014

Updated Tue Jan 21 15:20:19 PST 2014

This is a tentative calendar. I probably will have to move some things as we go along but I'll try to avoid moving the test days so you can plan ahead.

I will post homework assignments here so please check back often, at least once a week.

Chapter and section numbers refer to our textbooks

### Lectures and assignments

• 1st week, Jan. 20, 22
• Mon. Jan. 22 Rev. Martin Luther King Holiday
• Outline of the course: Integration, the Existence and Uniqueness Theorem of Ordinary Differential Equations (Picard's theorem), multivariable calculus and its connection with linear algebra, the Implicit Function Theorem and the Inverse Function theorem.
• 2nd week, Jan. 27, 29
• [Lebl] 5.1 The Riemann Integral
• 3rd week, Feb. 3, 5
• [Lebl] 3.4 Uniform continuity
• Homework Sec. 3.4 exercise 3.4.8, Sec. 5.1 exercise 5.1.11. Due Monday Feb 10.
• [Lebl] 5.3 Fundamental theorem of calculus.
• [Trench] Lemma 3.2.4 p. 131: Riemann's and Darboux' integrals are the same.
• [Lebl] 5.2 Properties of the Riemann Integral (lightly)
• [Lebl] 6.1 Sequences of functions: Pointwise and Uniform convergence. Example where continuous functions converge pointwise to discontinuous function: Fourier series for a step function.
• Homework: 6.1.2, 6.1.5, 6.1.6 (I found this one really surprising), 6.1.10, 6.2.1. Due Wednesday Feb. 12
• 4th week, Feb. 10, 12
• [Lebl] 6.2 Interchange of limits.
• [Lebl] 6.3 Picard's Theorem: existence and uniqueness of solutions of ordinary differential equations
• Slope field for van der Pol equation. Also see the Wikipedia article "van der Pol oscillator".
• 5th week, Feb. 17, 19
• Mon. Feb 17 Presidents' Day Holiday
• 6th week, Feb. 24, 26
• [Lebl] 6.3 Picard's Theorem: existence and uniqueness of solutions to ordinary differential equations
• Homework: #5.1.3, 5.1.4, 5.2.4, 5.2.5, 5.2.6. Due next Wednesday.
• 7th week, Mar. 3, 5
• Cancelled: Midterm Exam Monday March 3
• Homework 6.3.4 (easy!)
• Start chapter 7 (in the same book we have been using) Metric Spaces
• More homework (due in about a week). Exercises 7.1.3, 7.1.4, 7.1.6, 7.1.7
• 8th week, Mar. 10, 12
• [Trench] 5.1 Structure of $$\mathbb{R}^n$$. Vectors, open sets, Heine-Borel theorem.
• [Trench] 5.2 Continuous Real-valued functions of n variables.
• Homework: 5.1 exercises 7a, 9a, 12, 13, 19d, 24, 26, 29, 30, 5.2 exercise 3
• 9th week, Mar. 17, 19
• [Trench] 5.2 Continuous Real-valued functions of n variables.
• [Trench] 5.3 Partial derivatives and the differential. (Real-valued functions).
• 10th week, Mar. 24, 26
• [Trench] 5.3 Partial derivatives and the differential. (Real-valued functions).
• [Trench] 5.4 Chain rule, Taylor's theorem, Max-min. (Real-valued functions.)
• Mar. 31. Apr. 4 Spring Recess
• 11th week, Apr. 7, 9
• [Trench] 5.4 Chain rule, Taylor's theorem, Max-min. (Real-valued functions.)
• [Trench] 6.1 Linear Transformations and Matrices. (Linear algebra.)
• 12th week, Apr. 14, 16
• [Trench] 6.1 Linear Transformations and Matrices. (Linear algebra.)
• [Trench] 6.2 Differentiability, Chain Rule. (Vector-valued functions)
• Homework 6.2 exercises 5, 12ab, 20a
• 13th week, Apr. 21, 23
• [Trench] 6.2 Differentiability, Chain Rule. (Vector-valued functions)
• [Trench] 6.3 Inverse Function Theorem
• 14th week, Apr. 28, 30
• [Trench] 6.3 Inverse Function Theorem
• Homework Exercise 6.3 exercise 16. Hint: if you use complex variables then function is $$F(z)=z^2$$ because if $$z=(x+iy)$$ then $$z^2=(x^2-y^2)+i(2xy)=u(x,y)+iv(x,y)$$ where $$u$$ and $$v$$ are the functions in this problem.
• 15th week, May 5, 7
• [Trench] 6.3 Implicit Function Theorem
• Homework Exercise 6.4 #8
• Review
• Final exams week
• Final Exam Monday May 12, 4-6pm