AP Calculus AB is organized into 6 units (4 units in the first semester and 2 units in the second semester). The lessons in each unit include: Readings, Multimedia (lessons), Assignments, and Assessments. The course covers the principles of functions, derivatives, integrals, limits, approximation, and applications and modeling. Students will be able to: work with functions represented in a variety of ways; understand the connections among graphical, numerical, analytical, or verbal representations; understand the meaning of the derivative in terms of a rate of change and local linear approximation, and be able to use derivatives to solve a variety of problems; understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and use integrals to solve a variety of problems; understand the relationship between the derivative and the definite integral as expressed in both parts of the fundamental theorem of calculus.

Boundary layers as rational approximations to the solutions of exact equations of fluid motion. Physical parameters influencing laminar and turbulent aerodynamic flows and transition. Effects of compressibility, heat conduction, and frame rotation. Influence of boundary layers on outer potential flow and associated stall and drag mechanisms. Numerical solution techniques and exercises. The major focus of 16.13 is on boundary layers, and boundary layer theory subject to various flow assumptions, such as compressibility, turbulence, dimensionality, and heat transfer. Parameters influencing aerodynamic flows and transition and influence of boundary layers on outer potential flow are presented, along with associated stall and drag mechanisms. Numerical solution techniques and exercises are included.

Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology.

Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. Option A:chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology.

Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Analysis I covers Fundamentals of Mathematical Analysis: Convergence of Sequences and Series, Continuity, Differentiability, Riemann Integral, Sequences and Series of Functions, Uniformity, Interchange of Limit Operations. Three versions of the course are available. Each option shows the utility of abstract concepts and teaches understanding and construction of proofs. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and is for students with more mathematical maturity; it places more emphasis on Point-Set Topology and N-Space, whereas Option A is concerned primarily with the Real Line. Option C is a variant of Option B, with further instruction and practice in written and oral communication.

CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

CK-12 Calculus Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Calculus Student Edition. The solution guide is available upon request.

Introduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma. Stability of equilibria by Lyapunov's first and second methods. Feedback linearization. Application to nonlinear circuits and control systems. Alternate years. Description from course website: This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The videos were created by renowned mathematics professor Gilbert Strang who has taught at MIT since 1962.

The video series reviews the key topics and ideas of calculus with applications to real-life situations and problems
and then fully covers the concept of Derivatives.

This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include: Concepts of function, limits, and continuity, Differentiation rules, application to graphing, rates, approximations, and extremum problems; Definite and indefinite integration; Fundamental theorem of calculus; Applications of integration to geometry and science; Elementary functions; Techniques of integration; Approximation of definite integrals, improper integrals, and L'Hôpital's rule.

Differentiation and integration of functions of one variable, with applications. Concepts of function, limits, and continuity. Differentiation rules, application to graphing, rates, approximations, and extremum problems. Definite and indefinite integration. Fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Approximation of definite integrals, improper integrals, and L'Hospital's rule.

Differentiation and integration of functions of one variable, with applications. Concepts of function, limits, and continuity. Differentiation rules, application to graphing, rates, approximations, and extremum problems. Definite and indefinite integration. Fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Approximation of definite integrals, improper integrals, and L'Hospital's rule.

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.

Се дефинира гранична вредност (граница) и непрекинатост на функција од две променливи.