# OPEN CONTENT

## INTRODUCTION TO DIFFERENTIAL EQUATIONS

This course in differential equations covers standard approaches to solving first order ordinary differential equations along with associated qualitative analyses, second order linear differential equations and systems of differential equations. Examples and applications are drawn from the sciences and engineering.

## PROBLEM SOLVING AND MATHEMATICAL DISCOVERY

Students can learn about roughly a dozen problem techniques (such as, “draw a useful diagram”, “find a pattern”, amd consider cases) and explicitly look at problem solving in a number of major topic areas (such as Number Theory, Counting, Geometry).

## CALCULUS AND VECTORS

This material highlights derivatives of polynomial, rational, exponential, logarithmic, trigonometric functions,integral calculus, real-world applications, vectors, lines, and planes.

## CALCULUS FOR THE SCIENCES

This course in differential and integral calculus begins with a review of functions, introduces limits and explores the derivative both from a limit-based and rule-based approach, covering elementary functions and applications. Integration is introduced from the perspective of anti-differentiation, followed by coverage of Riemann sums and the Fundamental Theorems, definite and indefinite integrals and solution techniques. Arc length, area and volume integrals and other applications are introduced. Series and convergence are explored, followed by an introduction to differential equations. Finally, parametric curves and polar coordinates, and the basics of multivariable calculus are presented. Examples are drawn from applications in the sciences.

## EUCLIDEAN GEOMETRY

This course is designed to support instructors who are teaching elements of Euclidean geometry, from properties of triangles and circles to applications. The material is designed around building problem solving and proof skills.

## COLLEGE ALGEBRA

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

This course extends students' experience with functions. Students can investigate the properties of polynomial, rational, exponential, logarithmic, trigonometric and radical functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills.

## ALGEBRA AND TRIGONOMETRY

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

## EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS

Students will be presented with course material that encompasses exponential and sinusoidal functions, properties, transformations, and applications.

## INTRODUCTION TO FUNCTIONS

Students will experience a firm foundation in functions while exploring function notation, domain and range, transformations of functions, inverses of functions, inequalities, absolute values, and reciprocals.

## LINEAR RELATIONS AND ANALYTIC GEOMETRY

Course material that is comprised of lessons relating to linear and non-linear relations, solving linear equations and linear systems, analytic geometry, and statistics.

## MEASUREMENT, GEOMETRY, AND TRIGONOMETRY

This content pack includes course modules for students that cover the Pythagorean theorem, measurement of 2D figures and 3D solids, optimization, geometric relationships, triangle trigonometry, angles in standard position, and trigonometric identities.`

## NUMBER SENSE AND ALGEBRAIC EXPRESSIONS

This course material provides students with lessons to learn about exponent laws, manipulating expressions including polynomials, radical and rational expressions, and investigating prime factorization.

## NUMBERS, GEOMETRY, ALGEBRA AND DATA

Pre-built lessons that cover negative numbers and fractions, basic algebra through patterning, proportional reasoning, and other topics, polygons, circles, and triangles.

These lessons cover graphs and tables, standard, factored and vertex forms, algebra of quadratic relations, quadratic equations, and intersections of lines and parabolas.

## SEQUENCES, SERIES, AND FINANCIAL LITERACY

Lesson material that spans arithmetic and geometric sequences, financial applications including simple interest, compound interest, and annuities.

## INTRODUCTION TO CALCULUS

An introductory undergraduate course in differential and integral calculus composed of five units Limits, Derivatives, Applications of Derivatives, Integrals and Applications of Integrals.

## Free Course Content

Course content to inspire your online course delivery.

## Question Banks

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