# MAT1224

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
• Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
• Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
• Explain the relationship between differentiation and integration.
Week 1
1.5
• Recognize when to use integration by substitution.
• Use substitution to evaluate indefinite integrals.
• Use substitution to evaluate definite integrals.
Week 2
2.1
• Determine the area of a region between two curves by integrating with respect to the independent variable.
• Find the area of a compound region.
• Determine the area of a region between two curves by integrating with respect to the dependent variable.
Week 2
2.2
• Determine the volume of a solid by integrating a cross-section (the slicing method).
• Find the volume of a solid of revolution using the disk method.
• Find the volume of a solid of revolution with a cavity using the washer method.

Week 3
2.3
• Calculate the volume of a solid of revolution by using the method of cylindrical shells.
• Compare the different methods for calculating a volume of revolution.
Week 3
2.4
• Determine the length of a plane curve between two points.
• Find the surface area of a solid of revolution.
Week 4
2.5
• Determine the mass of a one-dimensional object from its linear density function.
• Determine the mass of a two-dimensional circular object from its radial density function.
• Calculate the work done by a variable force acting along a line.
• Calculate the work done in stretching/compressing a spring.
• Calculate the work done in lifting a rope/cable.
• Calculate the work done in pumping a liquid from one height to another.
• Find the hydrostatic force against a submerged vertical plate.

Week 4
2.6
• Find the center of mass of objects distributed along a line.
• Find the center of mass of objects distributed in a plane.
• Locate the center of mass of a thin plate.
• Use symmetry to help locate the centroid of a thin plate.

Week 5
3.1
• Recognize when to use integration by parts.
• Use the integration-by-parts formula to evaluate indefinite integrals.
• Use the integration-by-parts formula to evaluate definite integrals.
• Use the tabular method to perform integration by parts.
• Solve problems involving applications of integration using integration by parts.

Week 5
3.2
• Evaluate integrals involving products and powers of sin(x) and cos(x).
• Evaluate integrals involving products and powers of sec(x) and tan(x).
• Evaluate integrals involving products of sin(ax), sin(bx), cos(ax), and cos(bx).
• Solve problems involving applications of integration using trigonometric integrals.

Week 6
3.3
• Evaluate integrals involving the square root of a sum or difference of two squares.
• Solve problems involving applications of integration using trigonometric substitution.

Week 6
3.4
• Integrate a rational function whose denominator is a product of linear and quadratic polynomials.
• Recognize distinct linear factors in a rational function.
• Recognize repeated linear factors in a rational function.
• Recognize distinct irreducible quadratic factors in a rational function.
• Recognize repeated irreducible quadratic factors in a rational function.
• Solve problems involving applications of integration using partial fractions.
Week 7
3.7
• Recognize improper integrals and determine their convergence or divergence.
• Evaluate an integral over an infinite interval.
• Evaluate an integral over a closed interval with an infinite discontinuity within the interval.
• Use the comparison theorem to determine whether an improper integral is convergent or divergent.
Week 8
4.3
• Recognize separable differential equations.
• Use separation of variables to solve a differential equation.
• Develop and analyze elementary mathematical models.
Week 8
4.5
• Write a first-order linear differential equation in standard form.
• Find an integrating factor and use it to solve a first-order linear differential equation.
• Solve applied problems involving first-order linear differential equations.
Week 9
5.1
• Find a formula for the general term of a sequence.
• Find a recursive definition of a sequence.
• Determine the convergence or divergence of a given sequence.
• Find the limit of a convergent sequence.
• Determine whether a sequence is bounded and/or monotone.
• Apply the Monotone Convergence Theorem.
Week 10
5.2
• Write an infinite series using sigma notation.
• Find the nth partial sum of an infinite series.
• Define the convergence or divergence of an infinite series.
• Identify a geometric series.
• Apply the Geometric Series Test.
• Find the sum of a convergent geometric series.
• Identify a telescoping series.
• Find the sum of a telescoping series.
Week 10
5.3
• Use the Divergence Test to determine whether a series diverges.
• Use the Integral Test to determine whether a series converges or diverges.
• Use the p-Series Test to determine whether a series converges or diverges.
• Estimate the sum of a series by finding bounds on its remainder term.
Week 11
5.4
• Use the Direct Comparison Test to determine whether a series converges or diverges.
• Use the Limit Comparison Test to determine whether a series converges or diverges.
Week 11
5.5
• Use the Alternating Series Test to determine the convergence of an alternating series.
• Estimate the sum of an alternating series.
• Explain the meaning of absolute convergence and conditional convergence.

Week 12
5.6
• Use the Ratio Test to determine absolute convergence or divergence of a series.
• Use the Root Test to determine absolute convergence or divergence of a series.
• Describe a strategy for testing the convergence or divergence of a series.
Week 12
6.1
• Identify a power series.
• Determine the interval of convergence and radius of convergence of a power series.
• Use a power series to represent certain functions.
Week 13
6.2
• Combine power series by addition or subtraction.
• Multiply two power series together.
• Differentiate and integrate power series term-by-term.
• Use differentiation and integration of power series to represent certain functions as power series.
Week 14
6.3
• Find a Taylor or Maclaurin series representation of a function.
• Find the radius of convergence of a Taylor Series or Maclaurin series.
• Finding a Taylor polynomial of a given order for a function.
• Use Taylor's Theorem to estimate the remainder for a Taylor series approximation of a given function.
Week 15
7.1
• Plot a curve described by parametric equations.
• Convert the parametric equations of a curve into the form y=f(x) by eliminating the parameter.
• Recognize the parametric equations of basic curves, such as a line and a circle.

Week 15
7.2
• Find the slope of the tangent line to a parametric curve at a point.
• Use the second derivative to determine the concavity of a parametric curve at a point.
• Determine the area bounded by a parametric curve.
• Determine the arc length of a parametric curve.
• Determine the area of a surface obtained by rotating a parametric curve about an axis.