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Our math learning platform gives personalized feedback while you are solving math problems, by analysing your input and identifying where the potential mistakes are.

Adaptivity's role is improving how every learner experiences the course. The platform adapts your individual learning path depending on your specific knowledge level.

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Our randomized exercises allow for endless practicing. Unlike regular textbooks, our problems look a little different every time you try them.

College Calculus | Pre-Calculus | Calculus for Engineering | Differential Equations | Financial Arithmetic | Calculus for the Social Sciences | |
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Arithmetic | ||||||

Order of operations | ||||||

Integers | ||||||

Decimals | ||||||

Fractions | ||||||

Powers | ||||||

Expanding brackets | ||||||

Factoring | ||||||

Algebra | ||||||

Calculating with fractions | ||||||

Simplifying fractions | ||||||

Fractions with variables | ||||||

Binomial coefficients | ||||||

Pascal's triangle | ||||||

Factorials | ||||||

Sigma notation | ||||||

Applications of combinatorics | ||||||

Applications of algebra | ||||||

Formulas and graphs | ||||||

Substitutions | ||||||

Formulas, tables and graphs | ||||||

Linear equations | ||||||

Linear equations with a single unknown | ||||||

Fractional linear equations | ||||||

Equations with absolute values | ||||||

Systems of linear equations | ||||||

Linear equations of a line | ||||||

Two linear equations with two unknowns | ||||||

Quadratic equations | ||||||

ABC-formula | ||||||

Completing the square | ||||||

The quadratic equation | ||||||

Factorization | ||||||

Quadratic equations with one unknown | ||||||

Intersection of two parabolas | ||||||

Fractional equations | ||||||

Root equations | ||||||

Applications of quadratic equations | ||||||

Linear inequalities | ||||||

Linear inequalities | ||||||

Fractional linear inequalities | ||||||

Linear inequalities with absolute values | ||||||

One linear inequality with two unknowns | ||||||

Multiple linear inequalities with two unknowns | ||||||

Applications of linear inequalities | ||||||

Exponential and logarithmic functions | ||||||

Rules of exponential functions | ||||||

Equations with exponential functions | ||||||

Logarithmic functions | ||||||

Equations with logarithmic functions | ||||||

Exponential growth | ||||||

Translating functions | ||||||

Scaling functions | ||||||

Symmetry of functions | ||||||

Composing functions | ||||||

Applications of exponential and logarithmic functions | ||||||

End value and constant value | ||||||

Calculate interest and maturity | ||||||

Equivalent percentages | ||||||

Trigonometry | ||||||

Right-angled triangle | ||||||

Degrees and radians | ||||||

Differentiation | ||||||

Tangents to a curve | ||||||

Derivatives of polynomials and power functions | ||||||

Sum rule | ||||||

Product rule | ||||||

Quotient rule | ||||||

Chain rule for differentiation | ||||||

Derivatives of trigonometric functions | ||||||

Quotient rule for differentiation | ||||||

Derivatives of inverse functions | ||||||

The natural logarithm | ||||||

Derivatives of exponential and logarithmic functions | ||||||

Approximation | ||||||

Elasticity | ||||||

Applications of differentiation | ||||||

Set theory | ||||||

Sets | ||||||

Operations of sets | ||||||

Intervals | ||||||

Functions | ||||||

Composition of functions | ||||||

Operations for functions | ||||||

Range of functions | ||||||

Functions and graphs | ||||||

Injective functions | ||||||

Inverse of a function | ||||||

Power functions | ||||||

Equations and functions | ||||||

Applications of function | ||||||

Polynomials and rational functions | ||||||

Calculating with polynomials | ||||||

Linear polynomials | ||||||

Quadratic polynomials | ||||||

Factorization of polynomials | ||||||

GCD and LCM for of polynomials | ||||||

Euclidean algorithm polynomials | ||||||

Polynomial interpolation | ||||||

Rational functions | ||||||

Applications of polynomials and rational functions | ||||||

Trigonometric functions | ||||||

Definitions of sin and cos | ||||||

Right triangles and trigonometric functions | ||||||

Periodicity and trigonometric functions | ||||||

Calculating with trigonometric functions | ||||||

Tangent and cotangent | ||||||

Triangles and trigonometric functions | ||||||

Inverse trigonometric functions | ||||||

Limits | ||||||

Notion and rules of limits and infinity | ||||||

Limits of rational functions | ||||||

Horizontal & vertical asymptotes | ||||||

Oblique asymptotes | ||||||

Squeeze theorem for limits | ||||||

Limits of exponential functions | ||||||

Trigonometric limits | ||||||

Applications of limits | ||||||

Sequences and series | ||||||

The notion of sequence and series | ||||||

Arithmetic series | ||||||

The notion of sequence and series | ||||||

Convergence & Divergence | ||||||

Rules for limits of sequences | ||||||

Power series | ||||||

Length | ||||||

Applications of sequences and series | ||||||

Continuity | ||||||

Global minimum and maximum | ||||||

Continuous extension | ||||||

Min-max and intermediate value theorem | ||||||

Limits of continuous functions | ||||||

Rules for continuity | ||||||

Applications of continuity | ||||||

Analysis of functions | ||||||

Local minima and maxima | ||||||

The mean value theorem | ||||||

Monotonicity | ||||||

Higher derivatives | ||||||

Implicit derivatives | ||||||

Linear approximation | ||||||

Taylor series | ||||||

The L'HÃ´pital rule | ||||||

Applications of analysis of functions | ||||||

Integration | ||||||

Antiderivation | ||||||

Area | ||||||

Riemann sums | ||||||

Integral of a function | ||||||

Calculation for integrals | ||||||

Estimates of integrals | ||||||

Mean value theorem for integrals | ||||||

The fundamental theorem of calculus | ||||||

Applications of integration | ||||||

Multivariate functions | ||||||

Functions of two variables | ||||||

Visualizing bivariate functions | ||||||

Multivariate functions | ||||||

Partial derivatives | ||||||

Higher partial derivatives | ||||||

Stationary points | ||||||

Minimum, maximum, and saddle point | ||||||

Criteria for extrema and saddle points | ||||||

Convexity and concavity | ||||||

Applications of multivariate functions | ||||||

Applications of optimization | ||||||

Introduction to Differential equations | ||||||

The notion of differential equations | ||||||

Notations for ODEs | ||||||

Order and degree of an ODE | ||||||

Solutions of differential equations | ||||||

Linear ODEs | ||||||

Direction fields | ||||||

Direction fields | ||||||

Euler's method | ||||||

Autonomous ODEs | ||||||

Existence and uniqueness of solutions of ODEs | ||||||

Solution strategy on the basis of the slope field | ||||||

Separation of variables | ||||||

Differentials | ||||||

Differential forms and separated variables | ||||||

Solving ODEs by separation of variables | ||||||

Linear first-order differential equations | ||||||

Uniqueness of solutions of linear first-order ODEs | ||||||

Linear linear first-order ODE and integrating factor | ||||||

Solving linear first-order ODEs | ||||||

Linear second-order differential equations | ||||||

Uniqueness of solutions of linear 2nd-order ODEs | ||||||

Homogeneous linear 2nd-order ODEs with constant coefficients | ||||||

Solving homogeneous linear ODEs with constant coefficients | ||||||

The Ansatz | ||||||

Solution methods for lineair second-order ODEs | ||||||

The Wronskian of two differentiable functions | ||||||

Variation of constants | ||||||

From one to two solutions | ||||||

Solving linear second-order ODEs | ||||||

Systems of differential equations | ||||||

Systems of couples linear first-order ODEs | ||||||

Evaluating investments | ||||||

Accounting payback period | ||||||

Average accounting return | ||||||

Economic payback period | ||||||

Net present value | ||||||

Internal profitability |