A math based economics course designed to provide the skills needed to solve fundamental problems in both macroeconomics and microeconomics, by covering concepts in precalculus and calculus.

Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher dimensions. This course begins with a fresh look at limits and continuity, moves to derivatives and the process of generalizing them to higher dimensions, and finally examines multiple integrals (integration over regions of space as opposed to intervals). Upon successful completion of this course, the student will be able to: Define and identify vectors; Define and compute dot and cross-products; Solve problems involving the geometry of lines, curves, planes, and surfaces in space; Define and compute velocity and acceleration in space; Define and solve Kepler's Second Law; Define and compute partial derivatives; Define and determine tangent planes and level curves; Define and compute least squares; Define and determine boundaries and infinity; Define and determine differentials and the directional derivative; Define and compute the gradient and the directional derivative; Define, determine, and apply Lagrange multipliers to solve problems; Define and compute partial differential equations; Define and evaluate double integrals; Use rectangular coordinates to solve problems in multivariable calculus; Use polar coordinates to solve problems in multivariable calculus; Use change of variables to evaluate integrals; Define and use vector fields and line integrals to solve problems in multivariable calculus; Define and verify conservative fields and path independence; Define and determine gradient fields and potential functions; Use Green's Theorem to evaluate and solve problems in multivariable calculus; Define flux; Define and evaluate triple integrals; Define and use rectangular coordinates in space; Define and use cylindrical coordinates; Define and use spherical coordinates; Define and correctly manipulate vector fields in space; Evaluate surface integrals and relate them to flux; Use the Divergence Theorem (Gauss' Theorem) to solve problems in multivariable calculus; Define and evaluate line integrals in space; Apply Stokes' Theorem to solve problems in multivariable calculus; Properly apply Maxwell's Equations to solve problems. (Mathematics 103)

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB programming.

Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.

Precalculus I is designed to prepare you for Precalculus II, Calculus, Physics, and higher math and science courses. In this course, the main focus is on five types of functions: linear, polynomial, rational, exponential, and logarithmic. In accompaniment with these functions, you will learn how to solve equations and inequalities, graph, find domains and ranges, combine functions, and solve a multitude of real-world applications.

This course is oriented toward US high school students. Mathematics comes together in this course. You enter precalculus with an abundant array of experience in mathematics, and this course offers an opportunity to make connections among the big ideas you encountered earlier. It also assists you in developing fluency with the tools used in learning calculus.

Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity.  This leads to the study of complex numbers and linear transformations in the complex plane.  The teacher materials consist of the teacher pages including exit tickets, exit ticket solutions, and all student materials with solutions for each lesson in Module 1.

This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of calculus. Analysis lies at the heart of the trinity of higher mathematics algebra, analysis, and topology because it is where the other two fields meet. Upon successful completion of this course, the student will be able to: Use set notation and quantifiers correctly in mathematical statements and proofs; Use proof by induction or contradiction when appropriate; Define the rational numbers, the natural numbers, and the real numbers, and understand their relationship to one another; Define the well-ordering principle the completeness/supremum property of the real line, and the Archimedean property; Prove the existence of irrational numbers; Define supremum and infimum; Correctly and fluently manipulate expressions with absolute value and state the triangle inequality; Define and identify injective, surjective, and bijective mappings; Name the various cardinalities of sets and identify the cardinality of a given set; Define Euclidean space and vector space and show that Euclidean space is a vector space; Define the complex numbers and manipulate them algebraically; Write equations for lines and planes in Euclidean space; Define a normed linear space, a norm, and an inner product; Define metric spaces, open sets; define open, closed, and bounded sets; define cluster points; define density; Define convergence of sequences and prove or disprove the convergence of given sequences; Prove and use properties of limits; Prove standard results about closures, intersections, and unions of open and closed sets; Define compactness using both open covers and sequences; State and prove the Heine-Borel Theorem; State the Bolzano-Weierstrass Theorem; State and use the Cantor Finite Intersection Property; Define Cauchy sequence and prove that specific sequences are Cauchy; Define completeness and prove that Euclidean space with the standard metric is complete; Show that convergent sequences are Cauchy; Define limit superior and limit inferior; Define convergence of series using the Cauchy criterion and use the comparison, ratio, and root tests to show convergence of series; Define continuity and state, prove, and use properties of limits of continuous functions, including the fact that continuous functions attain extreme values on compact sets; Define divergence of functions to infinity and use properties of infinite limits; State and prove the intermediate value property; Define uniform continuity and show that given functions are or are not uniformly continuous; Give standard examples of discontinuous functions, such as the Dirichlet function; Define connectedness and identify connected and disconnected sets Construct the Cantor ternary set and state its properties; Distinguish between pointwise and uniform convergence; Prove that if a sequence of continuous functions converges uniformly, their limit is also continuous; Define derivatives of real- and extended-real-valued functions; Compute derivatives using the limit definition and prove basic properties of derivatives; State the Mean Value Theorem and use it in proofs; Construct the Riemann Integral and state its properties; State the Fundamental Theorem of Calculus and use it in proofs; Define pointwise and uniform convergence of series of functions; Use the Weierstrass M-Test to check for uniform convergence of series; Construct Taylor Series and state Taylor's Theorem; Identify necessary and sufficient conditions for term-by-term differentiation of power series. (Mathematics 241)

Further study of real numbers, their real-valued functions, and integration and differentiation of these functions through the analysis of Manifolds.

Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this unit you will review the various approaches to sketching graphs and lea

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

This course is designed to introduce the student to the study of Calculus through concrete applications. Upon successful completion of this course, students will be able to: Define and identify functions; Define and identify the domain, range, and graph of a function; Define and identify one-to-one, onto, and linear functions; Analyze and graph transformations of functions, such as shifts and dilations, and compositions of functions; Characterize, compute, and graph inverse functions; Graph and describe exponential and logarithmic functions; Define and calculate limits and one-sided limits; Identify vertical asymptotes; Define continuity and determine whether a function is continuous; State and apply the Intermediate Value Theorem; State the Squeeze Theorem and use it to calculate limits; Calculate limits at infinity and identify horizontal asymptotes; Calculate limits of rational and radical functions; State the epsilon-delta definition of a limit and use it in simple situations to show a limit exists; Draw a diagram to explain the tangent-line problem; State several different versions of the limit definition of the derivative, and use multiple notations for the derivative; Understand the derivative as a rate of change, and give some examples of its application, such as velocity; Calculate simple derivatives using the limit definition; Use the power, product, quotient, and chain rules to calculate derivatives; Use implicit differentiation to find derivatives; Find derivatives of inverse functions; Find derivatives of trigonometric, exponential, logarithmic, and inverse trigonometric functions; Solve problems involving rectilinear motion using derivatives; Solve problems involving related rates; Define local and absolute extrema; Use critical points to find local extrema; Use the first and second derivative tests to find intervals of increase and decrease and to find information about concavity and inflection points; Sketch functions using information from the first and second derivative tests; Use the first and second derivative tests to solve optimization (maximum/minimum value) problems; State and apply Rolle's Theorem and the Mean Value Theorem; Explain the meaning of linear approximations and differentials with a sketch; Use linear approximation to solve problems in applications; State and apply L'Hopital's Rule for indeterminate forms; Explain Newton's method using an illustration; Execute several steps of Newton's method and use it to approximate solutions to a root-finding problem; Define antiderivatives and the indefinite integral; State the properties of the indefinite integral; Relate the definite integral to the initial value problem and the area problem; Set up and calculate a Riemann sum; Estimate the area under a curve numerically using the Midpoint Rule; State the Fundamental Theorem of Calculus and use it to calculate definite integrals; State and apply basic properties of the definite integral; Use substitution to compute definite integrals. (Mathematics 101; See also: Biology 103, Chemistry 003, Computer Science 103, Economics 103, Mechanical Engineering 001)

This 16-minute video lesson discusses exponential growth involving bacteria (some calculus in part c).