Mathematics (All Of It)
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13 learners
What you'll learn
This course includes
- 25.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 193 lessons • 25.5 hours of video
Mathematics (All Of It)
193 lessons
• 25.5 hours
Mathematics (All Of It)
193 lessons
• 25.5 hours
- Introduction to Linear Algebra: Systems of Linear Equations10:46
- Understanding Matrices and Matrix Notation05:26
- Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination10:36
- Types of Matrices and Matrix Addition06:46
- Matrix Multiplication and Associated Properties06:22
- Evaluating the Determinant of a Matrix07:09
- The Vector Cross Product06:46
- Inverse Matrices and Their Properties12:00
- Solving Systems Using Cramer's Rule07:43
- Understanding Vector Spaces08:41
- Subspaces and Span05:50
- Linear Independence12:56
- Basis and Dimension10:06
- Change of Basis09:34
- Linear Transformations on Vector Spaces09:11
- Image and Kernel05:35
- Orthogonality and Orthonormality11:48
- The Gram-Schmidt Process10:07
- Finding Eigenvalues and Eigenvectors17:10
- Diagonalization08:43
- Complex, Hermitian, and Unitary Matrices09:00
- Further Matrix Decompositions: LU, Cholesky, QR, and SVD10:10
- Introduction to Algebra: Using Variables04:04
- Basic Number Properties for Algebra05:16
- Algebraic Equations and Their Solutions04:52
- Algebraic Equations With Variables on Both Sides06:46
- Algebraic Word Problems05:38
- Solving Algebraic Inequalities05:43
- Square Roots, Cube Roots, and Other Roots09:02
- Simplifying Expressions With Roots and Exponents08:23
- Solving Algebraic Equations With Roots and Exponents05:46
- Introduction to Polynomials05:13
- Adding and Subtracting Polynomials05:32
- Multiplying Binomials by the FOIL Method06:25
- Solving Quadratics by Factoring09:37
- Solving Quadratics by Completing the Square07:32
- Solving Quadratics by Using the Quadratic Formula06:55
- Solving Higher-Degree Polynomials by Synthetic Division and the Rational Roots Test09:22
- Manipulating Rational Expressions: Simplification and Operations09:30
- Graphing in Algebra: Ordered Pairs and the Coordinate Plane06:56
- Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts06:52
- Graphing Lines in Slope-Intercept Form (y = mx + b)05:06
- Graphing Lines in Standard Form (ax + by = c)05:33
- Graphing Parallel and Perpendicular Lines04:47
- Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination10:21
- Absolute Values: Defining, Calculating, and Graphing05:10
- What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational09:00
- Back to Algebra: What are Functions?07:23
- Manipulating Functions Algebraically and Evaluating Composite Functions05:29
- Graphing Algebraic Functions: Domain and Range, Maxima and Minima05:54
- Transforming Algebraic Functions: Shifting, Stretching, and Reflecting07:52
- Continuous, Discontinuous, and Piecewise Functions05:18
- Inverse Functions06:29
- The Distance Formula: Finding the Distance Between Two Points03:38
- Graphing Conic Sections Part 1: Circles07:46
- Graphing Conic Sections Part 2: Ellipses06:33
- Graphing Conic Sections Part 3: Parabolas in Standard Form08:30
- Graphing Conic Sections Part 4: Hyperbolas05:58
- Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros09:15
- Graphing Rational Functions and Their Asymptotes07:24
- Solving and Graphing Polynomial and Rational Inequalities07:34
- Evaluating and Graphing Exponential Functions05:59
- Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions08:10
- Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property06:26
- Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions07:06
- Solving Exponential and Logarithmic Equations07:08
- Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem08:35
- Set Theory: Types of Sets, Unions and Intersections06:22
- Sequences, Factorials, and Summation Notation11:12
- Theoretical Probability, Permutations and Combinations15:52
- Introduction to Mathematics06:44
- Addition and Subtraction of Small Numbers08:39
- Multiplication and Division of Small Numbers06:20
- Understanding Fractions, Improper Fractions, and Mixed Numbers06:13
- Large Whole Numbers: Place Values and Estimating04:29
- Decimals: Notation and Operations04:21
- Working With Percentages03:36
- Converting Between Fractions, Decimals, and Percentages05:21
- Addition and Subtraction of Large Numbers05:57
- The Distributive Property for Arithmetic03:19
- Multiplication of Large Numbers06:28
- Division of Large Numbers: Long Division05:41
- Negative Numbers05:27
- Understanding Exponents and Their Operations08:42
- Order of Arithmetic Operations: PEMDAS04:22
- Divisibility, Prime Numbers, and Prime Factorization05:54
- Least Common Multiple (LCM)05:40
- Greatest Common Factor (GCF)04:46
- Addition and Subtraction of Fractions04:07
- Multiplication and Division of Fractions05:06
- Analyzing Sets of Data: Range, Mean, Median, and Mode05:46
- Introduction to Geometry: Ancient Greece and the Pythagoreans04:00
- Basic Euclidean Geometry: Points, Lines, and Planes04:19
- Types of Angles and Angle Relationships07:24
- Types of Triangles in Euclidean Geometry05:25
- Proving Triangle Congruence and Similarity05:08
- Special Lines in Triangles: Bisectors, Medians, and Altitudes06:20
- The Triangle Midsegment Theorem03:08
- The Pythagorean Theorem05:02
- Types of Quadrilaterals and Other Polygons06:17
- Calculating the Perimeter of Polygons05:08
- Circles: Radius, Diameter, Chords, Circumference, and Sectors04:58
- Calculating the Area of Shapes06:39
- Proving the Pythagorean Theorem03:34
- Three-Dimensional Shapes Part 1: Types, Calculating Surface Area07:32
- Three-Dimensional Shapes Part 2: Calculating Volume06:17
- Introduction to Trigonometry: Angles and Radians06:27
- Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent07:18
- The Easiest Way to Memorize the Trigonometric Unit Circle09:48
- Basic Trigonometric Identities: Pythagorean Identities and Cofunction Identities05:25
- Graphing Trigonometric Functions11:40
- Inverse Trigonometric Functions06:54
- Verifying Trigonometric Identities09:14
- Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-Prod09:29
- Solving Trigonometric Equations08:28
- The Law of Sines05:14
- The Law of Cosines04:38
- Polar Coordinates and Graphing Polar Equations10:46
- Parametric Equations04:36
- Introduction to Calculus: The Greeks, Newton, and Leibniz08:40
- Understanding Differentiation Part 1: The Slope of a Tangent Line05:29
- Understanding Differentiation Part 2: Rates of Change05:31
- Limits and Limit Laws in Calculus12:49
- What is a Derivative? Deriving the Power Rule10:05
- Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule11:53
- Derivatives of Trigonometric Functions07:57
- Derivatives of Composite Functions: The Chain Rule12:29
- Derivatives of Logarithmic and Exponential Functions08:41
- Implicit Differentiation11:45
- Higher Derivatives and Their Applications07:29
- Related Rates in Calculus08:53
- Finding Local Maxima and Minima by Differentiation06:17
- Graphing Functions and Their Derivatives13:06
- Optimization Problems in Calculus10:55
- Understanding Limits and L'Hospital's Rule09:12
- What is Integration? Finding the Area Under a Curve08:18
- The Fundamental Theorem of Calculus: Redefining Integration09:38
- Properties of Integrals and Evaluating Definite Integrals09:48
- Evaluating Indefinite Integrals10:44
- Evaluating Integrals With Trigonometric Functions07:32
- Integration Using The Substitution Rule10:40
- Integration By Parts13:17
- Integration By Trigonometric Substitution15:55
- Advanced Strategy for Integration in Calculus16:13
- Evaluating Improper Integrals12:24
- Finding the Area Between Two Curves by Integration07:52
- Calculating the Volume of a Solid of Revolution by Integration11:20
- Calculating Volume by Cylindrical Shells07:40
- The Mean Value Theorem For Integrals: Average Value of a Function07:24
- Convergence and Divergence: The Return of Sequences and Series09:40
- Estimating Sums Using the Integral Test and Comparison Test09:56
- Alternating Series, Types of Convergence, and the Ratio Test12:08
- Power Series06:48
- Taylor and Maclaurin Series09:34
- Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses07:34
- Three-Dimensional Coordinates and the Right-Hand Rule06:41
- Introduction to Vectors and Their Operations10:17
- The Vector Dot Product06:59
- Double and Triple Integrals15:29
- Partial Derivatives and the Gradient of a Function10:57
- Vector Fields, Divergence, and Curl15:36
- Evaluating Line Integrals12:54
- Green's Theorem06:37
- Evaluating Surface Integrals12:24
- Stokes's Theorem08:11
- The Divergence Theorem06:31
- Introduction to Differential Equations04:34
- Classification of Differential Equations07:33
- Separable First-Order Differential Equations07:05
- Linear First-Order Differential Equations04:46
- Exact First-Order Differential Equations08:45
- Homogeneous Differential Equations and Bernoulli Differential Equations10:20
- Linear Second-Order Differential Equations Part 1: Homogeneous Case10:20
- Linear Second-Order Differential Equations Part 2: Non-Homogeneous Differential Equations10:18
- Special Second-Order Differential Equations: Cauchy-Euler, Nonlinear, and More09:37
- Numerical Methods for Solving Differential Equations08:30
- Power Series Solutions Part 1: Leibniz Method10:33
- Power Series Solutions Part 2: Frobenius Method09:24
- Systems of Differential Equations Part 1: Modeling and Elimination07:50
- Systems of Differential Equations Part 2: Matrices and Stability11:50
- Laplace Transforms Part 1: Solving Differential Equations07:58
- Laplace Transforms Part 2: Convolutions and LTI Systems14:59
- Difference Equations and Z-Transforms10:34
- Introduction to Partial Differential Equations: Classification and Differential Operators10:56
- Quasi-Linear First-Order Partial Differential Equations: Lagrange’s Method08:14
- Laplace’s Equation: Separation of Variables11:04
- Fourier Series and Transforms Part 1: Concepts in Frequency Analysis11:02
- Fourier Series and Transforms Part 2: Power Spectra and K-Space06:38
- The Wave Equation Part 1: Vibrations in 1D10:15
- The Wave Equation Part 2: Multidimensional Waves and Dispersion08:20
- The Diffusion Equation Part 1: Separation of Variables06:52
- The Diffusion Equation Part 2: Dimensional Analysis and Self-Similarity10:59
- The Diffusion Equation Part 3: Green’s Functions08:42
