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This is the standard sequence of Calculus that science, math, and other relative majors often take. At MSA we have all the necessary resources to help our students do
well in their Calculus courses.
Our specially developed approach to teaching this course, makes Calculus easy to understand and enjoyable to learn.
Limits, continuity, and differentiation of algebraic functions. Applications of differentiation; exponential, logarithmic, and trigonometric functions and their derivatives; the definite integral and the fundamental theorem of calculus. Application of the integral. The Riemann sum, Intermediate Value Theorem, Mean Value Theorem, L’Hospital’s rule and more.
Analytic geometry in three dimensions, vectors and vector functions, planes in three dimensions, chain rule, partial derivatives, and parametric equations. Gradient, delta-epsilon argument of limits of three variables. Continuity, differentiation, contour maps and level curves, equations to tangent planes and tangent vectors to a surface. Vector Analysis. Multiple integrals, line integrals, Lagrange multipliers and optimization questions. Cauchy-Schwartz inequality, The Triangle Inequality.
Calculus I - Differential Calculus
Limits, continuity, and differentiation of algebraic functions. Applications of differentiation; exponential, logarithmic, and trigonometric functions and their derivatives; the definite integral and the fundamental theorem of calculus. Application of the integral. The Riemann sum, Intermediate Value Theorem, Mean Value Theorem, L’Hospital’s rule and more.
Calculus II - Integral Calculus
Theoretical treatments and Applications of Definite Integrals. Techniques of Integration. Infinite sequences and series and convergence and divergence of series. Taylor Series and polynomial Approximations. Line integrals. Parametric equations and polar coordinates. Elementary differential equations. Basic proof methods.Multivariable Calculus - Calculus III
Analytic geometry in three dimensions, vectors and vector functions, planes in three dimensions, chain rule, partial derivatives, and parametric equations. Gradient, delta-epsilon argument of limits of three variables. Continuity, differentiation, contour maps and level curves, equations to tangent planes and tangent vectors to a surface. Vector Analysis. Multiple integrals, line integrals, Lagrange multipliers and optimization questions. Cauchy-Schwartz inequality, The Triangle Inequality.
