Difference between revisions of "MAT1193"

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(Starting table)
 
(Filling out the course map for MAT 1193 (Fall 20))
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! Date !! Section !! Topic !! Pre-requisite !! Student Learning Outcome
 
! Date !! Section !! Topic !! Pre-requisite !! Student Learning Outcome
 
|-
 
|-
−
| Week 1 || Example || Functions ||  
+
| Week 1 || '''Example''' || Functions
 +
||  
 
* Basic graphing skills and the idea of a function and graphs of elementary functions (lines, parabola) and understanding of slope
 
* Basic graphing skills and the idea of a function and graphs of elementary functions (lines, parabola) and understanding of slope
−
* Periodic functions || Example
+
* Periodic functions  
 +
||  
 +
* Define a function and connect to a real-world dynamical model
 +
* Estimate instantaneous rate of change by both visualization of average rate of change and calculations of the formula
 +
* Understand formulas for distance, velocity and speed and make connection with slope formula
 +
* 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
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 2 || '''Example''' || Instantaneous Rate of Change
 +
||  
 +
* Evaluating functions
 +
* Tangent lines
 +
* Average rate of change
 +
* Equations of a line (slope-intercept, point-slope)
 +
  ||  
 +
* Comparing and contrasting the average rate of change (ARC)  with instantaneous rate of change (IRC)
 +
* Defining velocity using the idea of a limit
 +
* Visualizing the limit with tangent lines
 +
* 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
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 3 || '''Example''' || Limits || '''Example'''
 +
||  
 +
* 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
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 4 || '''Example''' || Derivative Formulas (Derivatives for powers and polynomials)
 +
||  
 +
* Equations of lines
 +
* Composite functions
 +
||  
 +
* 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
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 4 || '''Example''' || Derivative Formulas (Derivatives for trigonometric functions)
 +
||  
 +
* Exponential
 +
* Logarithmic
 +
* Trigonometric
 +
* Applications
 +
||  
 +
* Differentiate trigonometric functions
 +
* Applications of trigonometric function derivatives
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Applications
 +
||  
 +
* Local & Global Maxima & Minima
 +
* Concavity
 +
||  
 +
* 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)
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 7 || '''Example''' || Accumulated Change & the Definite Integral
 +
||  
 +
* 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
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 8 || '''Example''' || 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
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 9 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Week 6 || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Example || '''Example''' || Example || Example || Example
 
|-
 
|-
−
| Example || Example || Example || Example || Example
+
| Example || '''Example''' || Example || Example || Example
 
|-
 
|-
 
| Example || Example || Example || Example || Example
 
| Example || Example || Example || Example || Example

Revision as of 13:29, 6 July 2020

Date Section Topic Pre-requisite Student Learning Outcome
Week 1 Example Functions
  • Basic graphing skills and the idea of a function and graphs of elementary functions (lines, parabola) and understanding of slope
  • Periodic functions
  • Define a function and connect to a real-world dynamical model
  • Estimate instantaneous rate of change by both visualization of average rate of change and calculations of the formula
  • Understand formulas for distance, velocity and speed and make connection with slope formula
  • 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
Week 2 Example Instantaneous Rate of Change
  • Evaluating functions
  • Tangent lines
  • Average rate of change
  • Equations of a line (slope-intercept, point-slope)
  • Comparing and contrasting the average rate of change (ARC) with instantaneous rate of change (IRC)
  • Defining velocity using the idea of a limit
  • Visualizing the limit with tangent lines
  • 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
Week 3 Example Limits Example
  • 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 Example Derivative Formulas (Derivatives for powers and polynomials)
  • Equations of lines
  • Composite functions
  • 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
Week 4 Example Derivative Formulas (Derivatives for trigonometric functions)
  • Exponential
  • Logarithmic
  • Trigonometric
  • Applications
  • Differentiate trigonometric functions
  • Applications of trigonometric function derivatives
Week 6 Example Applications
  • Local & Global Maxima & Minima
  • Concavity
  • 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 Example Accumulated Change & the Definite Integral
  • 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 8 Example 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 Example Example Example Example
Week 6 Example Example Example Example
Week 6 Example Example Example Example
Week 6 Example Example Example Example
Week 6 Example Example Example Example
Week 6 Example Example Example Example
Week 6 Example Example Example Example
Week 6 Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
Example Example Example Example Example
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