
College Calculus 
PreCalculus 
Calculus 
Calculus for the Social Sciences 
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





ABCformula 




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 




Trigonometry





Rightangled 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 




Minmax 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'Hôpital 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 



