Good fit for first and second-year math courses for university STEM majors

Contains polynomials, trigonometric functions, sequences and series, differentiation and more.

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- Propositional logic
- Propositions and truth
- Negation, conjunction, and disjunction
- Implication
- Compound propositions
- Propositions as variables
- Truth tables

- Calculating with propositions
- Equivalence
- Rules of calculation for propositions
- Order of operations
- Verum and Falsum

- Predicate logic
- Logical quantifiers
- Reasoning by induction

- Logical argumentation
- Methamtical proofs
- Modus ponens
- Substitution in logic
- Proof by contradiction

- Sets
- The notion of set
- Set builders
- Subsets
- Intervals

- Operations of sets
- Union and intersection of sets
- Rules of calculation of sets
- Difference and complement of sets
- Rules of calculation with set difference
- Cartesian product

- Relations
- The notion of relation
- Equivalence relation
- Graphs
- Functions

- Real numbers
- Properties of the real numbers
- Ordering of real numbers
- The notion of real number
- Ordering and decimal development
- Decimal developments of real numbers
- Calculating with real numbers

- Functions
- The notion of function
- Domain
- Functions and graphs
- The range of a function

- Operations for functions
- Arithmetic operations on functions
- Composition of functions

- Range
- Recognizing graphs
- Transformations of a graph
- Symmetry of functions

- Injectivity
- Injectivity
- Monotonic functions
- The inverse of a function
- Properties of inverse functions

- Applications
- Power functions
- Power functions & equations
- Equations and functions
- Substitution of equations

- Quadratic polynomials
- Linear functions
- Quadratic functions
- Quadratic equations
- Quadratic inequalities

- Polynomials
- The notion of polynomial
- Calculating with polynomials
- Division with remainder for polynomials
- Other representations of polynomials

- Greatest common divisor
- The notion of gcd for polynomials
- Rules of calculation for gcd of polynomials
- The Euclidean algorithm of polynomials
- The notion of lcm for polynomials
- The extended Euclidean algorithm for polynomials

- Factorisation of polynomials
- Factors and zeros
- Factorisation of polynomials
- The Fundamental Theorem of Algrebra
- Factorisation techniques

- Rational functions
- The notion of rational function
- Calculating with rational functions
- Standard form for rational functions
- Partial fraction decomposition for rational functions

- Other
- Polynomial interpolation

- The functions sine and cosine
- Unit circle and angles
- Sine and cosine
- Sinusoids
- Right-angled triangles and trigonometric funcitions
- Symmetry of trigonometric functions

- Calculating with sine and cosine
- Special values of trigonometric functions
- Addition formulas for trigonometric functions
- Triangles and trigonometric functions

- More trigonometric functions
- Tangent
- Reciprocal trigonometric functions
- Inverses of trigonometric functions

- Definition exp
- The notion of exponential function
- Rules of calculation for exponential functions
- Equations with exponential functions

- Definition log
- The notion of logarithm
- Rules of calculation for logarithms
- Equations with logarithms

- Growth
- Exponential growth

- Definition of limit
- The notion of limit
- Limits and infinity

- Calculating with limits
- Limits of rational functions
- Rules of arithmetic calculation with limits
- Composition rule for limits
- Sandwich rule for limits

- Asymptotes
- Vertical asymptotes
- Horizontal asymptotes
- Oblique asymptotes

- Limits of some non-rational functions
- Limits of exponential functions
- Limits of trigonometric functions
- Limits of inverse functions

- Definition of sequence and series
- The notions of sequence and series
- Arithmetic sequence and series
- Geometric series

- Limits of sequences
- Convergence of sequences
- Divergence of sequences
- Rules for limits of sequences
- Monotonic sequences

- Convergence of series
- Absolute convergence and ratio test for series
- Alternating and comparison test for series
- Consideration test for series

- Power series
- The notion of power series
- The natural exponential function
- Limits involving exponential functions

- Completeness of the real numbers
- Infima and superma for sets of real numbers
- Limits and superma
- Cauchy sequences

- Definition of continuity
- The notion of continuity
- Standard continuous functions
- Continuous extension

- Three theorems on continuous functions
- The Min-Max Theorem
- The Intermediate Value Theorem
- Uniform continuity

- Limits & continuity
- Limits and continuous functions
- Rules for continuity

- Continuity in geometry
- Curves in the plane
- Length of a curve
- Regions
- Area of a region

- Definition of differentiation
- The notion of difference quotient
- The notion of differentiation
- The derivative and the tangent

- Calculating derivatives and tangent lines
- Derivative of a power function
- Sum rule for differentiation
- Product rule for differentiation
- Chain rule for differentiation
- Quotient rule for differentiation
- Calculating tangent lines

- Derivatives of special functions
- Derivatives of trigonometric functions
- Derivatives of exponential functions
- Derivatives of inverse functions
- Derivatives of logarithmic functions

- Other
- The De L’Hôpital rule

- Minima and maxima
- Local minima and maxima
- The Mean Value Theorem
- Monotonocity

- Higher derivatives
- Higher derivatives
- Applications of higher derivatives

- Implicit derivatives
- Implicit derivatives
- Derivatives of bivariate functions
- Implicit function theorem
- Tangent line to a curve

- Approximation with polynomials
- Linear approximation
- Taylor series
- Taylor series of some known functions

- Antiderivatives
- The notion of an antiderivative
- Antiderivatives of some known functions

- Definite integrals
- Riemann sums
- The definite integral of a function
- Rules of calculation for integrals

- Properties of definite integrals
- Estimates of definite integrals
- The Mean Value Theorem for integrals
- The Fundamental Theorem of Calculus
- Improper integrals

- Calculating with definite integrals
- Area between graphs
- Length of a curve revisited
- Volume in space
- Series and integrals

- Finding antiderivatives
- Substitution method
- Trigonometric integrals
- Inverse substitution
- Integration by parts
- Integration by parts, advanced usage

- Antiderivatives of rational functions
- Known antiderivatives of rational functions
- Fraction decomposition for integration
- Existence of antiderivatives of rational functions
- Finding antiderivatives of rational functions