Calculus
MATH 2100, 2200, 3200, 4050, 4060
Fall 2024
Functions, limits, and derivatives of algebraic functions. Introduction to derivatives of trigonometric functions, logarithmic functions; application of derivatives to physics problems; related rates and maximum/minimum problems, and definite and indefinite integrals with applications.
Riemann sums; the definite integral; method of integration; continuation of exponential, logarithmic functions, and inverse trigonometric functions. L'Hopital's rule and improper integrals.
Functions of several variables, surfaces, in three-space, vectors, techniques of partial differentiation and multiple integration with applications. Vector calculus topics will include the theorems of Green, Gauss and Strokes.
The course is an introduction to the theoretical treatment of the real numbers, sets, functions, sequences, limits and calculus. The course places an emphasis on reading and writing formal mathematical proofs. Topics include: the real number system, convergence of sequence and series, continuity, limits, functions of one real variable, and the theoretical foundations of differentiation and integration of functions of a single variable.
This course is a continuation of Advanced Calculus I providing an introduction to metric spaces and their topology. The course places an emphasis on extending results for real functions to multivariable functions. Topics include: metric spaces and topology, integration, differentiation, optimization and analysis in several variables.
Required Textbooks for Calculus I, II (MATH 2100, 2200):
Calculus: Early Transcendentals by
For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics. The most successful new calculus text in the last two decades The much-anticipated 3rd Edition of Briggs' Calculus Series retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eBook contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts. For the 3rd Edition, the authors synthesized feedback on the text and MyLab(tm) Math content from over 140 instructors and an Engineering Review Panel. This thorough and extensive review process, paired with the authors' own teaching experiences, helped create a text that was designed for today's calculus instructors and students. Also available with MyLab Math MyLab Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0134995996 / 9780134995991 Calculus: Early Transcendentals and MyLab Math with Pearson eText - Title-Specific Access Card Package, 3/e Package consists of: 0134763645 / 9780134763644 Calculus: Early Transcendentals 0134856929 / 9780134856926 MyLab Math with Pearson eText - Standalone Access Card - for Calculus: Early Transcendentals
Call Number: QA303.2 .B75 2019ISBN: 9780134763644Publication Date: 2018-01-02
No required textbooks for Calculus III.
Required Textbooks for Advanced Calculus I, II (MATH 4050, 4060):
Introduction to Real Analysis by
This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.
Call Number: AVAILABLE FOR PURCHASE ONLINEISBN: 9780471433316Publication Date: 2011-01-18
- Describe the concept of limit of a function at a point and at infinity and the concept of continuity at a point and over an interval. Compute limits of sums, products, differences, and quotients of functions.
- Describe the relationship between line slope, rate change, and derivative and apply the definition of derivative to compute the derivative of a function.
- Compute derivatives of functions using the product, quotient, power and chain rules explicitly and implicitly.
- Use the second derivative to find intervals where a function is concave up/down.
- Describe how the integral came about and be able to compute areas under curves.
- Understand and apply differentiation rules to exponential and logarithmic functions as well as inverse trigonometric functions.
- Learn new techniques of integration by parts, integration by trigonometric substitution, and integration via a partial fraction decomposition and utilize them where appropriate.
- Apply the Fundamental Theorem of Calculus to solve a variety of applied problems such as the area between 2 curves, volumes of revolution, surface area, length of a curve, and problems involving the concept of work.
- Comprehend the fundamental concepts and differences between sequences and series of numbers and apply the appropriate tests to determine their convergence or divergence.
- Define and use vector operations in two and three dimensions.
- Demonstrate an understanding of partial derivatives and multiple integrals.
- Perform applications of partial derivatives and multiple integrals.
- Understand the fundamentals of vector space calculus including the Green, Gauss and Stokes theorems.
- Construct mathematically rigorous proofs of the real number line from the axioms for the field of real numbers.
- Utilize a rigorous approach to applying limits to problems on limits of sequences and functions.
- Apply the definition of derivative to prove elementary results of differentiation.
- Apply the definition of the Riemann integral to prove elementary properties of Riemann Integral and Fundamental Theorem of Calculus.
- Utilize the definition and topology of metric spaces and prove basic results of compactness.
- Apply the definition of derivatives in a multi-dimensional space to prove elementary results of differentiation.
- Demonstrate the pointwise and uniform convergence of infinite series of functions.
- Apply the integration in multi-variable spaces to prove basic results of line integrals.
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