Difference between revisions of "MAT1224"

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Revision as of 15:19, 6 August 2020

The textbook for this course is Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.

A comprehensive list of all undergraduate math courses at UTSA can be found here.

The Wikipedia summary of calculus and its history.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
1.3

The Fundamental Theorem of Calculus

  • Evaluate definite integrals using the Fundamental Theorem of Calculus
  • Interpret the definite integral as the signed area under the graph of a function.
Week 1
1.5


Integration by Substitution



  • Use substitution to evaluate indefinite integrals.
  • Use substitution to evaluate definite integrals.
Week 2
2.1

Area between Curves


  • Find the area of plane regions bounded by the graphs of functions.
Week 2
2.2

Determining Volumes by Slicing

  • Find the volume of solid regions with a known cross-sectional area.


Week 3
2.3

Volumes of Revolution, Cylindrical Shells

  • Find the volume of solid regions obtained by revolving a plane region about a line.


Week 3
2.4


Arc Length and Surface Area

  • Find the arc length of a plane curve
  • The area of the surface obtained by revolving a curve about one of the coordinate axes.


Week 4
2.5

Physical Applications

  • Find the mass of an object with a given density function.
  • Find the work done by a variable force
  • Find the work done in pumping fluid from a tank
  • Find the hydrostatic force on a vertical plate.


Week 4
2.6

Moments and Center of Mass

  • Find the moments and center of mass of a thin plate of uniform density.


Week 5
3.1

Integration by Parts

  • Integrate products of certain functions.
  • Integrate logarithmic and inverse trigonometric functions.


Week 5
3.2

Trigonometric Integrals

  • Integrate products of powers of sin(x) and cos(x) as well as sec(x) and tan(x).


Week 6
3.3

Trigonometric Substitution


  • Integrate the square root of a sum or difference of squares.


Week 6
3.4

Partial Fractions

  • Integrate rational functions whose denominator is a product of linear and quadratic polynomials.


Week 7
3.7

Improper Integrals

  • Recognize improper integrals and determine their convergence or divergence.


Week 7
4.3

Separation of Variables

  • Recognize and solve separable differential equations
  • Develop and analyze elementary mathematical models.


Week 8
2.8

Exponential Growth and Decay

  • The exponential growth model
  • The concept of doubling time
  • The exponential decay model
  • The concept of half-life


Week 8
4.4

The Logistic Equation

  • Carrying capacity in the logistic model of population growth
  • Interpret the solution curves of a direction field for a logistic equation
  • Solve a logistic equation and interpret the results


Week 9
5.1

Sequences

  • Find the formula for the general term of a sequence.
  • Discuss the convergence or divergence of a sequence.
  • Find the limit of a convergent sequence.
  • Determine whether a sequence is monotone.


Week 10
5.2

Infinite Series

  • Define the convergence or divergence of an infinite series.
  • Find the sum of a geometric or telescoping series.
Week 10
5.3

The Divergence and Integral Tests

  • Determine the convergence or divergence of a series using the Divergence or Integral Tests.
  • Estimate the sum of a series using the Remainder Estimate Theorem.


Week 11
5.4

Comparison Tests

  • Determine the convergence or divergence of a series using the Direct or Limit Comparison Tests.


Week 11
5.5

Alternating Series

  • Determine the convergence or divergence of alternating series.
  • Estimate the sum of an alternating series.
  • Describe the difference between conditional and absolute convergence.


Week 12
5.6

Ratio and Root Tests


  • Determine the convergence or divergence of infinite series using the ratio and root tests..


Week 12
6.1

Power Series and Functions

  • Recognize a power series.
  • Find its interval and radius of convergence.
  • Represent certain functions as power series.


Week 13
6.2

Properties of Power Series

  • Differentiate and integrate power series term-by-term.
  • Recognize certain continuous functions as power series on their radius of convergence.



Week 14
6.3

Taylor and Maclaurin Series

  • Find the Taylor or Maclaurin series representation of a function.
  • Find the radius of convergence of a Taylor Series.
  • Estimate the remainder in a Taylor polynomial approximation.



Week 15
7.1

Parametric Equations

  • Sketch the graph of a parametric curve


Week 15
7.2

The Calculus of Parametric Equations

  • Find the slope of the tangent line to a parametric curve at a point
  • Find the second derivative of a parametric curve
  • Determine the area bounded by a parametric curve
  • Determine the arc length of a parametric curve
  • Calculating the area of a surface obtained by rotating a parametric curve about an axis