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	Recognize when to use integration by substitution. Use substitution to evaluate indefinite integrals. Use substitution to evaluate definite integrals.
Week 2	2.1	Area between Curves	Graphing elementary functions The Definite Integral The Fundamental Theorem of Calculus Integration by Substitution	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 The Fundamental Theorem of Calculus Integration by Substitution	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 Determining Volumes by Slicing The Fundamental Theorem of Calculus Integration by Substitution	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 The Fundamental Theorem of Calculus Integration by Substitution	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, Hooke's Law) The Fundamental Theorem of Calculus Integration by Substitution	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 The Fundamental Theorem of Calculus Integration by Substitution	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	Differentiation Rules Differentials The Fundamental Theorem of Calculus Integration by Substitution	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. Integrate products of functions, logarithmic functions, and inverse trigonometric functions. Solve problems involving applications of integration using integration by parts.
Week 5	3.2	Trigonometric Integrals	Trigonometric Functions Trigonometric Identities The Fundamental Theorem of Calculus Integration by Substitution Integration by Parts	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	Trigonometric Substitution	Completing the Square Trigonometric Functions Trigonometric Identities Integration by Substitution Integration by Parts Trigonometric Integrals	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	Partial Fractions	Factoring Polynomials Completing the Square Long Division of Polynomials Systems of Linear Equations Antiderivatives Integration by Substitution	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	Improper Integrals	The Fundamental Theorem of Calculus Integration by Substitution Integration by Parts Trigonometric Integrals Trigonometric Substitution Partial Fractions The Limit Laws Limits at Infinity L’Hôpital’s Rule	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 7	4.3	Separation of Variables	Factoring Polynomials Exponential Properties Logarithmic Properties Differentials Initial-Value Problems Integration by Substitution Integration by Parts Trigonometric Integrals Trigonometric Substitution Partial Fractions	Recognize separable differential equations. Use separation of variables to solve a differential equation. Develop and analyze elementary mathematical models.
Week 8	2.8	Exponential Growth and Decay	Separation of Variables	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	Partial Fractions Separation of Variables Exponential Growth and Decay	Describe the concept of environmental carrying capacity in the logistic model of population growth. Solve a logistic equation and interpret the results.
Week 9	5.1	Sequences	The Limit Laws Limits at Infinity L’Hôpital’s Rule Increasing and Decreasing Functions	Find the formula for the general term 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.
Week 10	5.2	Infinite Series	Sigma notation Sequences Partial Fractions	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	Use the Divergence Test to determine whether a series converges or diverges. Use the Integral 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	Comparison Tests	Series Increasing and Decreasing Functions Infinite Limits	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	Alternating Series	Absolute Value Function Increasing and Decreasing Functions Infinite Limits	Use the Alternating Series Test to determine the convergence or divergence of an alternating series. Estimate the sum of an alternating series. Explain the meaning of absolute convergence and conditional convergence.
Week 12	5.6	Ratio and Root Tests	Factorials Infinite Limits Square root and Absolute value Functions	Use the Ratio Test to determine absolute convergence of a series. Use the Root Test to determine absolute convergence of a series. Describe a strategy for testing the convergence or divergence of a series.
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