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.
Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | Tu 11:15-12:15, We 10:00-11:00 in Research I, 107 |
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 |
Homework and Quizzes: | 20% |
Midterm Exam I: | 20% |
Midterm Exam II: | 20% |
Final Exam: | 40% |
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 |