Calculus

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Inverse Functions. Instructors may cover either Sections 6.2–6.4 or Sections 6.2*–6.4*. Exponential Functions and Their Derivatives. Logarithmic Functions. Derivatives of Logarithmic Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Inverse Trigonometric Functions. Applied Project: Where to Sit at the Movies. Hyperbolic Functions. Indeterminate Forms and l’Hospital’s Rule. Writing Project: The Origins of l’Hospital’s Rule. Review. Problems Plus. For those who wishes to learn advanced calculus, however, perhaps there is a need to peruse another text because in a way this text is not very close to real analysis; it is a broad text in terms of topic but the depth is not that much, though it does make an effort by not eliminating crucial proofs and explanations. CLP-4 Vector Calculus (Feldman, Rechnitzer, and Yeager) This textbook covers Vector Calculus. There are chapters on curves, vector fields, surface integrals and integral theorems (such as the divergence theorem). The Calculus of Functions of Several Variables (Sloughter) This textbook corresponds with a 300-level mathematics course taught at Furman University. Students should have completed four semesters of college level calculus prior to attempting this course. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Review. Principles of Problem Solving.

In short, this says, we have integral of a function over a domain. This is equal to antiderivative on boundary of domain. I'm attending a university and we are using a textbook from another author (Calculus 2nd Edition by Briggs, Cochran, and Gillet). The book I am using for school that is required is not that great because it is written as if you know your math pretty well. What I mean is, you are suppose to know formulas you might have not seen before. With Stewart he explains where you get the formulas from. Three-Dimensional Coordinate Systems. Vectors. Discovery Project: The Shape of a Hanging Chain. The Dot Product. The Cross Product. Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Planes. Discovery Project: Putting 3D in Perspective. Cylinders and Quadric Surfaces. Review. Problems Plus.

Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green’s Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes’ Theorem. The Divergence Theorem. Summary. Review. Problems Plus. Stewart's writing style speaks clearly and directly to students, guiding them through key ideas, theorems, and problem-solving steps, and encouraging them to think as they read and learn calculus. CLP-1 Differential Calculus (Feldman, Rechnitzer, and Yeager) This textbook covers single variable Differential Calculus. Supplemental Modules (Calculus) Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. Calculus has two primary branches: differential calculus and integral calculus. Multivariable calculus is the extension of calculus in one variable to functions of several variables. Vector calculus is a branch of mathematics concerned with differentiation and integration of vector fields. Modeling with Differential Equations. Direction Fields and Euler’s Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Models for Population Growth. Linear Equations. Applied Project: Which Is Faster, Going Up or Coming Down? Predator-Prey Systems. Review. Problems Plus.

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He conducted research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Dr. Stewart most recently served as a professor of mathematics at McMaster University, and his research focused on harmonic analysis. Dr. Stewart authored a best-selling calculus textbook series, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS and CALCULUS: CONCEPTS AND CONTEXTS as well as a series of successful precalculus texts. Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Review. Problems Plus. Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Kepler’s Laws. Review. Problems Plus. Overall, this book has been a solid resource while taking calculus classes in college. Using it in combination with other resources, I nailed straight A's despite not having taken a math class in 8 years. To other students and anyone interested, I highly recommend reading a few books on teaching. I am a physics tutor for my university and I read about teaching to prepare because I wanted to be a good tutor. As it turns out, I learned a lot that has actually made me a much better student.Numbers, Inequalities, and Absolute Values. Coordinate Geometry and Lines. Graphs of Second-Degree Equations. Trigonometry. Sigma Notation. Proofs of Theorems. Answers to Odd-Numbered Exercises. Calculus (OpenStax) The text guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical Coordinates. Discovery Project: The Intersection of Three Cylinders. Triple Integrals in Spherical Coordinates. Applied Project: Roller Derby. Change of Variables in Multiple Integrals. Review. Problems Plus. More challenging exercises called "Problems Plus" follow the end-of-chapter exercises. These sections reinforce concepts by requiring students to apply techniques from more than one chapter of the text, and by patiently showing them how to approach a challenging problem. PROBLEM-SOLVING EMPHASIS: George Polya’s problem-solving methodology is introduced at the beginning and reinforced throughout. "Strategies" sections help students select what techniques they'll need to solve problems in situations where the choice is not obvious and help them develop true problem-solving skills and intuition.