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	The Fundamental Theorem of Calculus	Differentiation Rules The Chain Rule Antiderivatives The Definite Integral	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	Integration by Substitution	Differentiation Rules Differentials Antiderivatives The Definite Integral The Fundamental Theorem of Calculus	Use substitution to evaluate indefinite integrals. Use substitution to evaluate definite integrals.
Week 2	2.1	Area between Curves	Graphing elementary functions Antiderivatives The Definite Integral The Fundamental Theorem of Calculus	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	Determining Volumes by Slicing	Areas of Basic Shapes Volume of a Cylinder Graphing elementary functions Antiderivatives The Definite Integral The Fundamental Theorem of Calculus	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	Volumes of Revolution, Cylindrical Shells	Graphing elementary functions Antiderivatives The Definite Integral The Fundamental Theorem of Calculus	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	Arc Length and Surface Area	Differentiation Rules Antiderivatives The Definite Integral The Fundamental Theorem of Calculus	Determine the length of a plane curve between two points. Find the surface area of a solid of revolution.
Week 4	2.5	Physical Applications	Areas of Basic Shapes Volume of a Cylinder Basic Physics (Mass, Force, Work, Newton's Second Law) Antiderivatives The Definite Integral The Fundamental Theorem of Calculus	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 pumping a liquid from one height to another. Find the hydrostatic force against a submerged vertical plate.
Week 4	2.6	Moments and Center of Mass	Graphing elementary functions Antiderivatives The Definite Integral The Fundamental Theorem of Calculus	Find the center of mass of objects distributed along a line. Locate the center of mass of a thin plate. Use symmetry to help locate the centroid of a thin plate.
Week 5	3.1	Integration by Parts	Antiderivatives Differentials Rules for finding Derivatives	Integrate products of certain functions. Integrate logarithmic and inverse trigonometric functions.
Week 5	3.2	Trigonometric Integrals	Integration by Substitution Solve trigonometric equations Trigonometric Identities	Integrate products of powers of sin(x) and cos(x) as well as sec(x) and tan(x).
Week 6	3.3	Trigonometric Substitution	Trigonometric Identities Integration by Substitution Trigonometric Integrals	Integrate the square root of a sum or difference of squares.
Week 6	3.4	Partial Fractions	Dividing Polynomials Antiderivatives Systems of Linear Equations Partial Fraction Decomposition	Integrate rational functions whose denominator is a product of linear and quadratic polynomials.
Week 7	3.7	Improper Integrals	Trigonometric Integrals Integration by Substitution Integration by Parts Limits of Functions Limits at Infinity	Recognize improper integrals and determine their convergence or divergence.
Week 7	4.3	Separation of Variables	Differentials Trigonometric Integrals Trigonometric Substitution Integration by Substitution Integration by Parts	Recognize and solve separable differential equations. Develop and analyze elementary mathematical models.
Week 8	2.8	Exponential Growth and Decay	Slope of a Line Equation of the tangent line Leibnitz notation of the derivative	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	Separable Equations Continuity Slope of a Line Exponential Growth and Decay	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	Infinite Limits Increasing and Decreasing Functions	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	Sigma notation Sequences	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	Continuity Antiderivatives When a Limit is Undefined Infinite Limits	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	Series Increasing and Decreasing Functions Infinite Limits	Determine the convergence or divergence of a series using the Direct or Limit Comparison Tests.
Week 11	5.5	Alternating Series	Absolute Value Function Increasing and Decreasing Functions Infinite Limits	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	Factorials Infinite Limits Square root and Absolute value Functions	Determine the convergence or divergence of infinite series using the ratio and root tests..
Week 12	6.1	Power Series and Functions	Polynomials Continuity Series Ratio and Root Tests	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	Indefinite integrals The Limit Laws Power Series and Functions	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	The Derivative of a Function Power Series and Functions Properties of Power 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	Trigonometric Functions Exponential Functions Sketching Common Functions	Sketch the graph of a parametric curve
Week 15	7.2	The Calculus of Parametric Equations	Parametric Equations The Derivative as a Function Integration by Substitution The Definite Integral	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