Lectures

(Figures in parentheses refer to sections of the corresponding books:
TF- Calculus - Thomas & Finney, Pearson Addison Wesley, Custom edition for the University of Pennsylvania
PS- Probability and Statistics- Morris DeGroot & Mark J. Schervish, Third Edition
FM- Finite Mathematics, Margaret Lial, Raymond N. Greenwall & Nathan P. Ritchey.)

Lecture 1: 05/16/2006
Some generalities about the course.
A (not-so) quick journey through "Calculus of one variable".
Discuss some problems from HW #1A.

Lecture 2: 05/17/2006
A review of trigonometric functions.
Limits and continuity of functions of one variable.

Lecture 3: 05/18/2006
Open and closed sets.
Functions of several variables. (FM; 12.1)

Lecture 4: 05/22/2006
Introduction to Limits and Continuity. (FM; 12.2)
Quiz #1.

Lecture 5: 05/23/2006
More limits. (FM; 12.2)
Partial derivatives. (FM; 12.3)

Lecture 6: 05/24/2006
Partial derivatives (continued). (FM; 12.3)
Linearization of a function of several variables. (FM; 12.4)

Lecture 7: 05/25/2006
Error in standard linear aproximation. (FM; 12.4)
Differentials, and predicting change using differentials. (FM; 12.4)
The Chain Rule (FM; 12.5)

05/29/2006: No class- Memorial Day!

Lecture 8: 05/30/2006
Review of vectors and elementary vector calculus.
Directional derivatives, gradient vectors. (FM; 12.7)
Review for Exam #1.

Lecture 9: 05/30/2006
Exam #1.
Directional derivatives, gradient vectors (continued). (FM; 12.7)

Lecture 10: 06/01/2006
Extreme values and saddle points. (FM; 12.8)

Introduction to Probability.

Lecture 11: 06/05/2006
Tangent planes. (FM; 12.7)
Extreme values and saddle points (continued). (FM; 12.8)

Lecture 12: 06/06/2006
Lagrange multipliers. (FM; 12.9)

Permutations and Combinations recalled.
The Definition of Probability. (PS; 1.5)
Finite Sample Spaces. (PS; 1.6)
Quiz #2.

Lecture 13: 06/07/2006
Permutations and Combinations recalled (continued).
Counting methods. (PS; 1.7)
Combinatorial methods. (PS; 1.8)
The Probability of a Union of events. (PS; 1.10)

Lecture 14: 06/08/2006
Multinomial coefficients. (PS; 1.9)
The Definition of Conditional Probability. (PS; 2.1)

Lecture 15: 06/12/2006
Multinomial coefficients (continued). (PS; 1.9)
The Definition of Conditional Probability (continued). (PS; 2.1)
Independent Events. (PS; 2.2)

Lecture 16: 06/13/2006
Bayes' Theorem. (PS; 2.3)
Random Variables and Discrete Distribution. (PS; 3.1)
Continuous Distribution. (PS; 3.2)
Review for Exam #2.

Lecture 17: 06/14/2006
Exam #2.
Continuous Distribution and the Probability Distribution function. (PS; 3.2)

Lecture 18: 06/15/2006
The Probability Distribution Function (continued). (PS; 3.2)
The Distribution Function. (PS; 3.3)
The Expectation of a Random Variable. (PS; 4.1)

Lecture 19: 06/19/2006
Properties of Expectations. (PS; 4.2)
Variance. (PS; 4.3)
Equations and slopes of line. (FM; 1.1)
The Least Squares Line. (FM; 1.3)
Addition and Subtraction of Matrices. (FM; 2.3)
Multiplication of Matrices. (FM; 2.4)
Quiz #2.

Lecture 20: 06/20/2006
Solution of Linear Systems by the Echelon Method. (FM; 2.1)
Solution of Linear Systems by the Gauss-Jordan Method. (FM; 2.2)
Matrix Inverses. (FM; 2.5)

Lecture 21: 06/21/2006
Review for Final Exam.

Lecture 22: 06/22/2006
Final Exam.
End of Course.

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Page last updated: 22^nd June 2006
Maintained by: Shuvra Gupta.