Course info

Department of Mathematics

School of Science

Manhattan College

 

Course Syllabus for MATH 156 – Calculus for the Life Sciences II

 

 

 

Semesters Offered:        Fall & Spring                                   Credit Hours:   3   (Meets four hours per week.)

 

Course Description:  Applications chosen from the life sciences, including population, decay, growth models, stability, and matrix methods. Volumes of solids, integration techniques, difference/differential equations.

 

Prerequisites:  A grade of C or higher in MATH 155: Calculus for the Life Sciences I

 

Student Learning Outcomes:  Upon successful completion of this course, the student will be able to:

·       Calculate antiderivatives yielding certain algebraic, rational, exponential, logarithmic, trigonometric functions.

·       Interpret the definite integral analytically and geometrically.

·       Demonstrate an understanding of the Fundamental Theorem of Calculus.

·       Solve basic area problems using definite integrals.

·       Use the standard techniques of integration such as integration by substitution, parts, and partial fractions.

·       Apply numerical integration techniques and understand the advantages or disadvantages of the different methods.

·       Calculate volumes of solids of revolution and evaluate improper integrals.

·       Compute various matrix calculations including solving linear systems, addition/subtraction, multiplication, determinants, inverses, eigenvalues and eigenvectors.

·       Use discrete dynamical systems and matrix methods to model long term trends in stratified populations.

·       Solve a variety of ordinary differential equations including separable, linear first-order, linear and nonlinear systems.

·       Use ordinary differential equations to solve application problems.

 

At least one of the following outcomes should be included:

 

·       Understand concepts from multivariable calculus such as partial differentiation, optimization, and double integration.

·       Understand the difference between discrete and continuous random variables. Apply basic probabilistic concepts to genetics.

 

Text: Calculus for the Life Sciences, 2nd Edition, by R. Greenwell, N. Ritchey, and M. Lial, Pearson, 2015. (with MyMathLab). Each student should have a graphing calculator either a TI 84 or TI 86 or equivalent; but no CAS calculators are accepted.

 

 

Course Outline, Possible Timeline:

 

1.       Review/Additional Topics from Calculus I             (2 weeks)

·       Antiderivatives

·       Substitution

·       Area and the Definite Integral

·       The Fundamental Theorem of Calculus

·       The Area Between Two Curves

 

 

2.       Integration Techniques and Applications                            (3 weeks)

 

·       Integration by Parts

·       Integration by Partial Fractions

·       Volume and Average Value

·       Improper Integrals (Review: Limits at Infinity)

 

3.       Multivariable Calculus                  (3 weeks)

 

·       Functions of Several Variables

·       Partial Derivatives

·       Maxima and Minima

·       Total Differentials and Approximations (if time permits)

·       Double Integrals

 

 

4.        Matrices            (3 weeks)

 

·       Solution of Linear Systems

·       Addition and Subtraction of Matrices

·       Multiplication of Matrices

·       Matrix Inverses

·       Eigenvalues and Eigenvectors

 

5.        Differential Equations                  (3 weeks)

 

·       Solutions of Elementary and Separable Differential Equations

·       Linear First-Order Differential Equations

·       Euler's Method

·       Linear Systems of Differential Equations

·       Nonlinear Systems of Differential Equations

·       Applications of Differential Equations

 

 

 

If time permits, we may cover some topics in Probability.

 

6.       Probability        

 

·       Sets

·       Introduction to Probability

·       Conditional Probability; Independent Events; Bayes’ Theorem

·       Discrete Random Variables; Applications to Decision Making

·       Continuous Probability Models

·       Expected Value and Variance of Continuous Random Variables

·       Special Probability Density Functions (if time permits)

 

 

Assessment of Student Learning Outcomes and Grading:

 

There will be 3 or four in-class exams, a comprehensive final exam, approximately one quiz per week, on-line homework assignments. The Final grade will be calculated in the following way:

 

In-class Exams                  56% (14% each if we have 4) If 3 exams, each will be 17%, for a total of 51%

Final Exam                        24%

Quizzes                              10%  if 4 exams, otherwise if 3 exams, quizzes will count 15%.

Homework                       10%

 

Course Policies:

 

This course has a common final exam.  Electronic homework (e.g., MyMathLab) is encouraged when applicable to the textbook being used.