Fall Semester 2010

Engineering and Science Mathematics 1A


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The courses from the ESM 1 series provide the foundation for all other Engineering and Science Mathematics courses, and taking at least one of them is mandatory for all Engineering and Science majors. Emphasis is on the use of basic mathematical concepts and methods in the sciences, rather than on detailed proofs of the underlying mathematical theory.

The course ESM 1A covers the basic differential and integral calculus of functions of one variable. It starts with a brief review of number systems and elementary functions, then introduces limits (for both sequences and functions) and continuity, before derivatives and differentiation with applications (tangent problem, error propagation, minima/maxima, zero-finding, curve sketching) are covered. A short chapter introduces complex numbers. The second half of the semester is devoted to integration (anti-derivatives and Riemann integral) with applications, and concluded by brief introductions to scalar separable and linear first order differential equations, and the convergence of number and power series.

In contrast to ESM 1C, which covers similar material, this course assumes a rigorous high school preparation in Mathematics, and leaves more room for explaining mathematical concepts (as needed for the majority of SES majors) rather than only developing skills for solving standard problems.

Contact Information:
Instructor:Marcel Oliver
Office hours:  Tu 11:15-12:15, We 10:00-11:00 in Research I, 107

Time and Place:
Lectures:  Tu 9:45-11:00, Th 8:15-9:30 in the Research II Lecture Hall
Tutorial I:  Tu 15:45-17:00 in the Research I Lecture Hall/CS Lab
Tutorial II:  We 13:00-14:15 in the Research I Lecture Hall/CS Lab

Recommended Textbooks:

The final grade will be computed as a grade point average with the following weights:
Homework and Quizzes:20%
Midterm Exam I:20%
Midterm Exam II:  20%
Final Exam:40%

Homework and Quizzes:

Missed Work:
Late homework will not be accepted under any circumstances as it poses undue burden on the instructor and the graders. For missed exams standard Jacobs policies apply.

Class Schedule

Note: the Section numbers in the class schedule refer to the 5th edition of Edwards & Penney. I will update to the current 6th edition as we go along.
02/09/2010: Section 1 Elementary concepts, functions and their graphs
07/09/2010: Sections 2.2-3, 11.1-2 Limits of functions and sequences
09/09/2010: Section 2.4 Continuity, introduction to the derivative
14/09/2010: Sections 3.1-2 Derivatives, differentiation rules
16/09/2010: Sections 3.3-4, 3.7, 7.1 Chain rule, derivatives of elementary functions
21/09/2010: Sections 3.5-6, 3.8 Applications: minimum/maximum, equation solving by iteration
23/09/2010: Sections 4.1-2 Implicit differentiation, differentials (linear approximation, errors)
28/09/2010: Sections 4.3-4.6 Curve sketching
30/09/2010: Review for Midterm I
05/10/2010: Midterm I
07/10/2010: Section 10.1 Complex numbers, polar coordinates, trigonometric form of complex numbers
12/10/2010: Sections 5.1-4 Introduction to integration
14/10/2010: Sections 5.5-6, 8.2 Fundamental theorem of calculus, substitution
21/10/2010: Sections 9.1-9.3 Techniques of integration I
26/10/2010: Sections 9.4-5 Techniques of integration II
28/10/2010: Sections 9.6-8 Techniques of integration III; improper integrals
02/11/2010: Sections 6.1-3 Applications of integrals I: Volumes of solids of revolution
04/11/2010: Section 6.3 Applications of integrals II: Arclength and surface area of revolution
09/11/2010: Review for Midterm II
11/11/2010: Midterm II in the Conrad Naber Lecture Hall
16/11/2010: Section 6.5 Ordinary differential equations I: separable differential equations
18/11/2010: Sections 6.6, 7.5 Ordinary differential equations II: force and work, natural growth and decay
23/11/2010: Sections 9.5, 11.2 Ordinary differential equations III: bounded growth
25/11/2010: Sections 11.3-4 Infinite series, Taylor series
30/11/2010: Sections 11.5-7 Convergence tests
02/12/2010: TBA
07/12/2010: Review for final exam
13/12/2010: Final Exam, Conference Hall & Eastwing

Last modified: 2010/11/10
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2010/esm101/index.html
Marcel Oliver (m.oliver@jacobs-university.de)