MATH 103: Biological Mathematics Summer 2016
Prerequisites Number of Credit hours Restrictions
None 3
Not open to students who have credit for MATH 101
Textbook Title: Applied Calculus, 5th Edition Authors: Hughus-Hallet / Gleason/ Lock/ Flath / et al. Publisher: John Wiley & Sons Inc., 2014
Course Topics Topics include functions and graphs; slopes; limits; continuity; derivatives; implicit differentiation; use of derivatives in graphing and applications; anti-derivative; definite and indefinite integrals; applications of the definite integrals; functions of several variables; partial derivatives
Course Objectives The course is mainly open to students in the biological sciences, where they have a need to utilize the concepts of calculus, and adapt and apply its ideas and techniques to functions represented by graphs or tables. Within this framework, the course aims for the following.
1. Discuss the basic elementary functions (linear, polynomial, rational, exponential, logarithmic, periodic, and trigonometric) that appear frequently or have great utility in life and biological sciences. 2. Develop the skills to model social, life, or biology related data through the basic elementary functions, which includes data fitting. 3. Treat limits and continuity from the intuitive, descriptive, graphical, numerical, and algebraic points of view.
4. Introduce the concept of a derivative as an instantaneous rate of change, discuss its graphical estimation, and establish the various rules of differentiation including the chain rule and implicit differentiation.
5. Emphasize some uses of the derivative, including graph sketching and solving problems of singlevariable optimization.
6. Discuss the concept of a definite integral as an accumulative change along with its numerical approximation, properties, interpretations in different contexts, and crown the discussion with the Fundamental Theorem of Calculus.
7. Present the concept of anti-derivative from a graphical, numerical and analytical point of view, and discuss integration by substitution.
8. Introduce functions of two variables and the idea of partial derivative. 9. Stress on applications that are drawn from biological and medical sciences.
Detailed Description and Estimated Lecture-hours Assignment 1.
FUNCTIONS: ● Linear functions ● Polynomials and rational functions ● Exponential and the natural logarithmic functions ● Operations on functions
9 hours
2.
RATE OF CHANGE (The derivative): Average rate of change and the slope ● The derivative function ● Linear approximation of functions ● Second and higher derivatives ● An intuitive approach to limits of functions
6 hours
3.
DIFFERENTIATION: ● The symbolic definition of the derivative ● Rules of differentiation ● The chain rule ● Higher order derivative
6 hours
4.
APPLICATIONS OF THE DERIVATIVE: ● Finding extrema ● Graph sketching ● Optimization ● Related rates
6 hours
5.
INTEGRATION: (a) Anti-derivatives (indefinite integral)
3 hours
● The definition of anti-derivative ● Integration by substitution (b) Accumulated Change (The Definite Integral)
6 hours
● Definite integral ● Fundamental theorem of Calculus ● Numerical approximation of definite integral ● Applications 6.
PARTIAL DIFFERENTIATION: ● Functions of two variables and their graphs ● Partial derivatives
3 hours
7.
EXAMS AND REVIEW
2 hours TOTAL
41 hours
Homework & Quizzes Homework in this course is assigned to help students learn the material, conceptually and practically, and to prepare for quizzes and exams. Homework is announced weekly either in class or on the course website. Although homework is not collected nor graded, it is important for students to work on homework problems in order to master the course (and consequently do well on quizzes and exams). Students are encouraged to ask questions, seek help and discuss problems with the instructor during office hours. There will also be weekly in-class quizzes except during midterm weeks. These are very short (5- to 10minute) quizzes covering material from the most recent assigned homework.
Assessment Method 1. 2. 3. 4.
Quizzes/Homework Project Midterm exams Comprehensive final exam
20% 10% 40% 30% Total 100%
There will be two midterm examinations during the instruction period. There will also be a major project to be assigned to groups of students and assessed through a written report. The details of this project will be announced on the course website in due course.