Calculus for the Biosciences
MAT 1193 Calculus for the Biosciences. (30) 3 Credit Hours. (TCCN = MATH 2313)
Prerequisite: MAT 1093 or an equivalent course or satisfactory performance on a placement examination. An introduction to calculus is presented using discretetime dynamical systems and differential equations to model fundamental processes important in biological and biomedical applications. Specific topics to be covered are limits, continuity, differentiation, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, differential equations, and the phaseplane. (Formerly MAT 1194. Credit can be earned for only one of the following: MAT 1193, MAT 1194, or MAT 1214.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $72; LRC1 $12; LRS1 $45; STSI $21.
Date 
Topic 
Prerequisite 
Student Learning Outcome

Week 1 
Review of Functions and Change


 Define a function and connect to a realworld dynamical model
 Identify the parts of linear functions (slope, yintercept).
 Demonstrate how to manipulate fractions.
 Identify power functions and polynomials.
 Identify exponential functions and their graphs in terms of exponential growth/decay.
 Identify logarithmic functions, graph and solve equations with log properties.
 Analyze graphs of the sine and cosine by recognizing amplitude and period.
 Identify and compute composite functions.

Week 2 
Instantaneous Rate of Change

 Evaluating functions
 Tangent lines
 Average rate of change
 Equations of a line (slopeintercept, pointslope)

 Compute the average rate of change (ARC).
 Compute the instantaneous rate of change (IRC)
 Comparing and contrasting ARC with IRC
 Defining velocity using the idea of a limit
 Visualizing the limit with tangent lines

Week 3 

Example

 Recognize graphs of derivatives from original function
 Estimate the derivative of a function given table data and graphically
 Interpret the derivative with units and alternative notations (Leibniz)
 Use derivative to estimate value of a function
 Use the limit definition to define the derivative at a particular point and to define the derivative function
 Distinguish the definition of continuity of a function
 Apply derivatives to biological functions

Week 4 & 5 
Derivative Formulas


 Use constant formula and power formula to differentiate functions along with the sum and difference rule
 Use differentiation to find the equation of a tangent line to make predictions using tangent line approximation
 Differentiate exponential and logarithmic functions
 Differentiate composite functions using the chain rule
 Differentiate products and quotients
 Differentiate trigonometric functions
 Applications of trigonometric function derivatives

Week 6 
Applications of Derivatives


 Detecting a local maximum or minimum from graph and function values
 Test for both local and global maxima and minima using first derivative test (finding critical points)
 Test for both local and global maxima and minima using second derivative test (testing concavity)
 Using concavity for finding inflection points
 Apply max and min techniques in real world applications in the field of Biology (logistic growth)

Week 7 
Accumulated Change

 Distance formula
 Summation formulas

 Approximate total change from rate of change
 Computing area with Riemann Sums
 Apply concepts of finding total change with Riemann Sums

Week 7 
The Definite Integral


 Approximate total change from rate of change
 Computing area with Riemann Sums
 Apply concepts of finding total change with Riemann Sums

Week 8 
Antiderivatives 
Basics in graphing

 Use the limit formula to compute a definite integral
 Be able to analyze area under the curve with antiderivatives graphically and numerically
 Use formulas for finding antiderivatives of constants and powers
 Use formulas for finding antiderivatives of exponential and logarithm functions
 Use formulas for finding antiderivatives of trigonometric functions

Week 9 
The Fundamental Theorem of Calculus 
Average formula

 Use the limit formula to compute a definite integral
 Compute area with the fundamental theorem of calculus (FTC)

Week 10 
Applications of Integrals 
Example 
Solve various biology applications using the fundamental theorem of calculus

Week 11 
Integration by Substitution 
Example 
Applying integration by substitution formulas

Week 12 
Integration by Parts 
Example

 Applying integration by integration by parts formulas
 Recognize which integration formulas to use

Week 13 
Differential Equations (Mathematical Modeling) 
Word problem setup and understanding of mathematical models

 Demonstrate how to take information to set up a mathematical model
 Examine the basic parts of differential equations

Week 14 
Differential Equations 
Graphing and factoring

 Examine differential equations graphically with slope fields
 Use separation of variables for solving differential equations

Week 15 
Differential Equations Applications 
Exponential functions

 Apply differential equations to exponential growth & decay functions for population models
 Apply differential equations to surge functions for drug models
 Modeling the spread of a disease
