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