Difference between revisions of "MAT1193"

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(→‎Calculus for the Biosciences: Agreed on SLOs for week 1 - Review)
(→‎Calculus for the Biosciences: Refined week 2 to limit the conversation to ARC and IRC)
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* Equations of a line (slope-intercept, point-slope)
 
* Equations of a line (slope-intercept, point-slope)
 
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* Comparing and contrasting the average rate of change (ARC) with instantaneous rate of change (IRC)
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* Understand the average rate of change (ARC).
 +
* Understand the instantaneous rate of change (IRC)
 +
* Comparing and contrasting ARC with IRC
 
* Defining velocity using the idea of a limit
 
* Defining velocity using the idea of a limit
 
* Visualizing the limit with tangent lines
 
* Visualizing the limit with tangent lines
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| Week 3 || [[Limits]]
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||
 +
'''Example'''
 +
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* Recognize graphs of derivatives from original function
 
* Recognize graphs of derivatives from original function
 
* Estimate the derivative of a function given table data and graphically
 
* Estimate the derivative of a function given table data and graphically
 
* Interpret the derivative with units and alternative notations (Leibniz)
 
* Interpret the derivative with units and alternative notations (Leibniz)
 
* Use derivative to estimate value of a function
 
* Use derivative to estimate value of a function
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| Week 3 || [[Limits]] || '''Example'''
 
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* Use the limit definition to define the derivative at a particular point and to define the derivative function
 
* Use the limit definition to define the derivative at a particular point and to define the derivative function
 
* Understand the definition of continuity  
 
* Understand the definition of continuity  

Revision as of 14:34, 27 August 2021

Calculus for the Biosciences

MAT 1193 Calculus for the Biosciences. (3-0) 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 discrete-time 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 phase-plane. (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 Pre-requisite Student Learning Outcome
Week 1 Review of Functions and Change
  • Define a function and connect to a real-world dynamical model
  • Understand the parts of linear functions (slope, y-intercept). Understand how to manipulate fractions.
  • Understand power functions and polynomials.
  • Understand exponential functions and their graphs in terms of exponential growth/decay.
  • Understand logarithmic functions, graph and solve equations with log properties.
  • Analyze graphs of the sine and cosine by understanding amplitude and period.
  • Understand composite functions.
Week 2 Instantaneous Rate of Change
  • Evaluating functions
  • Tangent lines
  • Average rate of change
  • Equations of a line (slope-intercept, point-slope)
  • Understand the average rate of change (ARC).
  • Understand 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 Limits

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
  • Understand the definition of continuity
  • 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
  • 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
  • Summation formulas
  • Approximate total change from rate of change
  • Computing area with Riemann Sums
  • Apply concepts of finding total change with Riemann Sums
  • Use the limit formula to compute a definite integral
  • Interpreting the definite integral as area above and below the graph
  • Use the definite integral to compute average value
Week 8 Antiderivatives Basics in graphing
  • 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 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)
  • Interpreting the definite integral as area above and below the graph
  • Use the definite integral to compute average value
Week 10 Integration Applications Example Solve various biology applications using the fundamental theorem of calculus
Week 11 Substitution Method Example Applying integration by substitution formulas
Week 12 Integration by Parts and further applications 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
  • Understand 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