MAC 2311 (sec 12942): Calculus - Analytic Geometry I
The course provides an introduction to standard techniques from calculus with a single variable. The main focus is on the concepts and computation of limits, derivatives and integrals. The course covers Chapters 2-5 of the book Single Variable Calculus, Early Transcendentals (James Stewart, 5th edition, Thomson Brooks/Cole, 2003), which below will be denoted by [Ste03]. The following topics are to be addressed:
- Concept of limit, definition and calculation of limits
- Tangents, velocities, and other rates of change
- Concept of a differentiable function
- Derivatives of polynomials and exponential functions
- Computing the derivative of products and quotients
- Applications, trigonometric functions
- Chain rule for derivatives
- Implicit differentiation
- Higher derivatives, logarithmic and hyperbolic functions
- Computing minima and maxima of functions
- Mean value theorem, l'Hospital's rule
- Graphing curves
- Applications
- Concept of the integral, fundamental theorem of calculus
- Substitution rule for integrals
More information on the course is available in the syllabus.
So far the following topics have been addressed in class:
- Aug 21-Aug 25, 2006: Limits and continuous functions
Literature: [Ste03, Ch. 2.1-2.3, Ch. 2.5]
- Aug 28, 2006: Intermediate value theorem
Literature: [Ste03, Ch. 2.5]
- Aug 30 *** class canceled due to tropical storm Ernesto ***
- Aug 31-Sep 1, 2006: Limits at infinity: vertical asymptotes
Literature: [Ste03, Ch. 2.6]
- Sep 6, 2006: The concept of a differentiable function, computing derivatives of polynomials
Literature: [Ste03, Ch. 2.8, Ch. 2.9, Ch. 3.1]
- Sep 7, 2006: Product and Quotient rule for computing derivatives
Literature: [Ste03, Ch. 3.2]
- Sep 8, 2006: Chain rule for computing derivatives
Literature: [Ste03, Ch. 3.5]
- Sep 11, 2006: Differentiation of exponential functions, implicit differentiation, derivative of ln(x)
Literature: [Ste03, Ch. 3.5, Ch. 3.6, Ch. 3.8]
- Sep 13, 2006: the number e as a limit, logarithmic differentiation,
Homework #1
Literature: [Ste03, Ch. 3.8]
- Sep 14, 2006: the exponential function as a limit, derivatives of logarithmic functions, implicit differentiation
Literature: [Ste03, Ch. 3.7, Ch. 3.8]
- Sep 15, 2006: logarithmic differentiation, implicit differentiation, derivatives of inverse trigonometric functions, higher derivatives
Literature: [Ste03, Ch. 3.6, Ch. 3.7, Ch. 3.8]
- Sep 18, 2006: hyperbolic functions
Literature: [Ste03, Ch. 3.9]
- Sep 20, 2006: extreme value theorem, Fermat's theorem, second derivative test
Literature: [Ste03, Ch. 4.1, Ch. 4.3]
- Sep 21, 2006: Rolle's theorem, mean value theorem
Literature: [Ste03, Ch. 4.2]
- Sep 22, 2006: applications of the mean value theorem, first derivative test
Literature: [Ste03, Ch. 4.2, Ch. 4.3]
- Sep 25, 2006: inflection points
Literature: [Ste03, Ch. 4.3]
- Sep 27, 2006: sketching a graph based on information on the derivatives
Literature: [Ste03, Ch. 4.3]
- Sep 28, 2006: graphing functions
Literature: [Ste03, Ch. 4.3]
- Sep 29, 2006: l'Hospital's rule, Exam #1
Literature: [Ste03, Ch. 4.4]
- Oct 2, 2006: l'Hospital's rule
Literature: [Ste03, Ch. 4.4]
- Oct 4, 2006: l'Hospital's rule: indeterminate differences and powers
Literature: [Ste03, Ch. 4.4]
- Oct 5, 2006: Newton's Method
Literature: [Ste03, Ch. 4.9]
- Oct 6, 2006: antiderivatives
Literature: [Ste03, Ch. 4.10]
- Oct 9, 2006: principle of mathematical induction, the area problem
Literature: [Ste03, Ch. 5.1, Appendix E]
- Oct 11, 2006: the definite integral
Literature: [Ste03, Ch 5.2]
- Oct 12, 2006: Fundamental Theorem of Calculus; Homework #2 is now online
Literature: [Str03, Ch. 5.3]
- Oct 13, 2006: presentations from Exam #1; indefinite integrals
Literature: [Str03, Ch. 5.4]
- Oct 16, 2006: substitution rule for integrals
Literature: [Str03, Ch. 5.5]
- Oct 18, 2006: substitution rule for integrals
Literature: [Str03, Ch. 5.5]
- Oct 19, 2006: substitution rule for integrals
Literature: [Str03, Ch. 5.5]
- Oct 20, 2006: an application of calculus in geometry
Literature: [Str03, Ch 2.3, Ex. 60]
- Oct 23, 2006: an application of the intermediate value theorem
Literature: [Str03, Ch. 2.5, Ex. 63]
- Oct 25, 2006: computing a tangent passing through a point outside the graph
Literature: [Str03, Ch. 3.2, Ex. 41]
- Oct 26, 2006: orthogonal curves; computing the position of a lamp
Literature: [Str03, Ch 3.6, Ex. 44, Ex. 69]
- Oct 27, 2006: rates of change
Literature: [Str03, Ch. 3.3, Example 1, Ch. 3.10, Example 5]
- Oct 30, 2006: optimization problems
Literature: [Str03, Ch. 4.7]
- Nov 1-Nov 6, 2006: applications of integration
Literature: [Str03, Ch. 6]
- Nov 8, 2006: an optimization problem
Literature: [Str03, Ch. 4.7, Example 4]
- Nov 9, 2006: optimization problems; Homework #3 is now online
Literature: [Str03, Ch. 4.7, Example 5, Exercise 1]
- Nov 13, 2006: exercises for l'Hospital's rule
Literature: [Str03, Ch. 4.4]
- Nov 15-20, 2006: repetition and exercises to prepare for the final exam
- Nov 22, 2006: final exam X2
My sincere thanks to all course participants for their contributions and participation. Thanks for patiently bearing with all the imperfections of the course!
For questions or comments, please feel free to contact me anytime
(see my homepage for email, phone number, etc.).
Dec 10, 2006