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	Antiderivatives The Definite Integral	Evaluate definite integrals using the Fundamental Theorem of Calculus Interpret the definite integral as the signed area under the graph of a function.
Week 1/2	1.5	Integration by Substitution	Solving Basic Integrals The Derivative of a Function Change of Variables	Use substitution to evaluate indefinite integrals. Use substitution to evaluate definite integrals.
Week 3	1.2	Area between Curves	Graphs of elementary functions, including points of intersection. Antiderivatives	Find the area of plane regions bounded by the graphs of functions.
Week 3/4	2.2	Determining Volumes by Slicing	Sketch the graphs of elementary functions Areas of basic Shapes Solving Basic Integrals	Find the volume of solid regions with a known cross-sectional area.
Week 4	2.3	The Shell Method	Sketch the graphs of elementary functions Solving Basic Integrals	Find the volume of solid regions obtained by revolving a plane region about a line.
Week 4/5	2.4	Arc Length and Surface Area	Sketch the graphs of elementary functions Solving Basic Integrals	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 5/6	2.5	Physical Applications	Solving Basic Integrals Knowledge of basic physics (e.g. mass, force, work).	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 6/7	2.6	Moments and Center of Mass	Sketching Common Functions Solving Basic Integrals	Find the moments and center of mass of a thin plate of uniform density.
Week 6	3.1	Integration by Parts	Antiderivatives Knowledge of Differentials Rules for finding Derivatives	Integrate products of certain functions. Integrate logarithmic and inverse trigonometric functions.
Week 7	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 7/8	3.3	Trigonometric Substitution	Trigonometric Identities Integration by Substitution Trigonometric Integrals	Integrate the square root of a sum or difference of squares.
Week 6/7	3.8	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 8	4.1	Basics of Differential Equations	The Derivative as a Function Differentiation Rules Implicit Differentiation	Classify an Ordinary Differential Equation according to order and linearity. Verify that a function is a solution of an Ordinary Differential Equation or an initial value problem.
Week 8/9	4.2	Direction Fields and Numerical Methods	Slope of a Line Equation of the tangent line Leibnitz notation of the derivative	Sketch the direction field of a first-order ODE(Ordinary Differential Equation) by hand Using direction field, find equilibria of an autonomous ODE. Determine the stability of equilibria using a phase line diagram.
Week 9	4.3	Separable Equations	Trigonometric Integrals Integration by Substitution Integration by Parts Linear Approximations and Differentials	Recognize and solve separable differential equations Develop and analyze elementary mathematical models.
Week 10/11	4.4	Exponential Growth and Decay, The Logistic Equation	Separable Equations Continuity Slope of a Line Find Equalibria and determine their Stability	Solve the exponential growth/decay equations and the logistic equation. Describe the differences between these two models for population growth.
Week 11	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 11/12	5.2	Series	Sigma notation Sequences	Define the convergence or divergence of an infinite series. Find the sum of a geometric or telescoping series.
Week 12	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 13/14	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 14	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 15	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 15/16	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 16	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 17	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 17/18	7.1	Parametric Equations	Trigonometric Functions Exponential Functions Sketching Common Functions	Sketch the graph of a parametric curve