Fall Semester 2015

Applied Calculus


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This course provides an introduction to calculus for students in the life science, applied engineering, and humanity and social science majors.

In comparison to Calculus, Applied Calculus will cover some advanced calculus topics in lesser depth and instead place more emphasis on connecting calculus concepts with experimental or observational data. To this end, the course includes, to a small degree, working with a mathematical software environment based on Scientific Python.

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 III Lecture Hall
Tutorial I:  Mo 15:45-17:00 in the Research II Lecture Hall
Tutorial II:  Mo 20:00-21:15 in the Research II Lecture Hall

Recommended Textbooks:

The semester is devided into two halfs with separate grades. In the first half-semester, the grade is compted as an averaged percent score with the following weights:
Midterm Exam I:30%
Midterm Exam II:  30%

In the second half-semester, the grade is compted as an averaged percent score with the following weights:
Midterm Exam III:30%
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. Similarly, missed quizzes cannot be retaken. For missed exams standard Jacobs policies apply.

Class Schedule

01/09/2015: Introduction; elementary statistical concepts. (MLS, Chapter 1)
03/09/2015: Fitting lines and higher degree polynomicals to data; least square fit (without derivation). (MLS, Chapter 3)
08/09/2015: Correlation coefficient, coefficient of determination; introduction to exponential and logarithmic functions. (MLS, Chapter 3 ctd., Chapter 4 started)
10/09/2015: Allometric (power law) relationships, rescaling data (log-log and semilog graphs). (MLS, Chapter 4 ctd.)
15/09/2015: Limits of functions. (MLS, Chapter 15)
17/09/2015: Continuity. (MLS, Chapter 16)
22/09/2015: Intermediate value theorem; limits and continuity in modeling contexts; Midterm review.
24/09/2015: Midterm I
29/09/2015: Discussion of midterm exam.
01/10/2015: Derivative, product rule, chain rule. (MLS, Chapter 18+19 in parts)
06/10/2015: Derivative as rate of change, velocity, average velocity; linear approximation (equation for tangent line). (MLS, Chapter 17)
08/10/2015: Local Extrema, necessary and sufficient conditions, points of inflection, curve sketching (MLS, Chapter 20 in parts)
13/10/2015: Curve sketching ctd.; midterm review (MLS, Chapter 20 ctd.)
15/10/2015: Midterm II
20/10/2015: No class (Reading Days)
22/10/2015: Midterm discussion; trigonometric functions; differentiation of inverse functions
27/10/2015: Minimization and maximization on closed intervals; applied mini-max problems (start, MLS, Section 20.7)
29/10/2015: Applied mini-max problems (ctd.)
03/11/2015: Review for midterm exam
05/11/2015: Midterm III
10/11/2015: Functions of several variables: partial derivatives, critical points (see Hoffmann/Bradley, "Calculus for Business, Economics, and the Social and Life Sciences", Chapter 7 Section 3; no second derivative test, but the derivation of the equations for a list square fit was covered)
12/11/2015: Lagrange multipliers (see Hoffmann/Bradley, "Calculus for Business, Economics, and the Social and Life Sciences", Chapter 7 Section 4)
17/11/2015: Error/uncertainty propagation in one and several variables (see lecture notes on the subject)
19/11/2015: Error/uncertainty propagation: sums and products of variables with independent errors; from average rates of change to the Fundamental Theorem of Calculus (MLS, Chapter 21 in part, Section 22.1)
24/11/2015: Examples for the Fundamental Theorem of Calculus, antiderivatives and indefinite integrals, integration by substitution (MLS, Sections 22.2-4, Section 23.1)
26/11/2015: Integration by parts, estimating integrals via the trapezoidal rule (MLS, Section 23.2, last two pages of Section 21.1)
01/12/2015: Simple differential equations (separable scalar first order equations): exponential growth, logistic growth, and some related examples (MLS, Chapter 25, some examples from Section 26.1)
03/12/2015: Review for final exam
19/12/2015: Final Exam, 9:00-11:00, Conference Hall/East Wing

Last modified: 2015/12/02
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2015/esm106/index.html
Marcel Oliver (m.oliver@jacobs-university.de)