MATH 2413 Fall 2010 Archive
David Milovich

Assistant Professor of Mathematics
Dept. of Engineering, Mathematics, and Physics
Texas A&M International Univerisity
Office: Canseco Hall, 313C
Email: david.milovich@tamiu.edu

Textbook

Syllabus
08/24/10 lecture notes: circles, domains, |x| (1.1, 1.2).
08/25/10 lecture notes: lines, slopes (1.3)
08/26/10 lecture notes: introduction to hyperreals (1.4)
08/30/10 lecture notes: principles of hyperreals (1.5)
08/31/10 lecture notes: standard parts (1.6)
09/01/10 lecture notes: slopes of curves (2.1)
09/02/10 lecture notes: the derivative (2.1)
09/06/10 lecture notes: power rule, sum rule, derivatives in motion and economics (2.3)
09/07/10 lecture notes: tangent lines; visualizing derivatives (2.2)
Graphs and formulas of common derivatives I
09/08/10 lecture notes: differentials, increment theorem (2.2)
09/09/10 lecture notes: product rule (2.3)
09/13/10 lecture notes: more power rules, reciprocal rule, quotient rule, population rate of change (2.3)
Proof of reciprocal rule with similar triangles I
Proof of reciprocal rule with similar triangles II
Proof of reciprocal rule with similar triangles III
09/14/10 lecture notes: inverse function rule (2.4)
09/15/10 lecture notes: inverse function rule (2.4)
09/16/10 lecture notes: derivatives of sine and cosine (2.5)
special angles
graphs of sine and cosine waves
sine and cosine symmetries I
sine and cosine symmetries II
09/20/10 lecture notes: derivatives of exponential, logarithm, and (more) trigonometric functions (2.5)
logarithm and exponentiation rules
Graphs and formulas of common derivatives II
09/21/10 lecture notes: review for midterm I
09/23/10 lecture notes: chain rule (2.6)
09/27/10 lecture notes: dy/dx=(dy/dt)/(dx/dt) (2.6)
Summary of differentiation rules
09/28/10 lecture notes: chain rule, higher derivatives (2.6, 2.7)
09/29/10 lecture notes: implicit differentiation (2.8)
09/30/10 lecture notes: related rates (3.2)
10/04/10 lecture notes: related rates (3.2)
10/05/10 lecture notes: limits (3.3)
10/06/10 lecture notes: one-sided limits (3.3)
logarithms and exponentiation rules for hyperreals
Some basic limit rules
10/07/10 lecture notes, version A: limits with exponentials and logarithms
10/07/10 lecture notes, version B: limits with exponentials and logarithms
Examples of limits, most with logarithms and exponentials
10/11/10 lecture notes, version A: continuity (3.4)
10/12/10 lecture notes, including version B of 10/11/10 notes: continuity (3.4)
10/13/10 lecture notes: intermediate value theorem (3.8)
10/14/10 lecture notes: extreme value theorem, Rolle's theorem, mean value theorem (3.8)
10/18/10 lecture notes: finding extrema over closed intervals
A tricky limit involving logarithms
Using hyperreal intervals to find minima and maxima
10/19/10 lecture notes: finding extrema over other intervals
10/20/10 lecture notes: single-critical-point methods for finding extrema (3.5)
10/21/10 lecture notes: optimization (3.6)
10/25/10 lecture notes: optimization (3.6)
10/26/10 lecture notes: review for midterm II
10/26/10 lecture notes supplement I
10/26/10 lecture notes supplement II
10/26/10 lecture notes supplement III
10/28/10 lecture notes: infinite limits (5.1)
11/01/10 lecture notes: limits at infinity (5.1)
11/02/10 lecture notes: L'Hospital's rule (5.2)
11/03/10 lecture notes: increasing, decreasing, concavity (3.6)
Proof of positive 2nd derivative implying concave up
11/04/10 lecture notes: increasing, decreasing, concavity
Concavity, and increasing/decreasing summary
11/08/10 lecture notes: local extrema
11/09/10 lecture notes: horizontal and vertical asymptotes (5.3)
11/10/10 lecture notes: Riemann sums and integrals (4.1)
11/11/10 lecture notes: Fundamental Theorem of Calculus (4.2)
11/15/10 lecture notes: sum rule, power rule for integrals (4.3)
11/16/10 lecture notes: trigonometric, logarithmic, and exponential antiderivatives (4.3)
11/17/10 lecture notes: integrals in motion and economics
11/18/10 lecture notes: integration by substitution (4.4)
11/22/10 lecture notes: integration by substitution (4.4), continuous averages
11/23/10 lecture notes: continuous averages, epsilon-delta definition of limits (5.8)
11/29/10 lecture notes: review I
11/30/10 lecture notes: review II
12/01/10 lecture notes: review III
12/02/10 lecture notes: review IV