Mathematics (All Of It)
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What you'll learn
This course includes
- 25.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 158 lessons • 25.5 hours of video
Mathematics (All Of It)
158 lessons
• 20 hours
Mathematics (All Of It)
158 lessons
• 20 hours
- Introduction to Linear Algebra: Systems of Linear Equations 10:46
- Understanding Matrices and Matrix Notation 05:26
- Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination 10:36
- Types of Matrices and Matrix Addition 06:46
- Matrix Multiplication and Associated Properties 06:22
- Evaluating the Determinant of a Matrix 07:09
- The Vector Cross Product 06:46
- Inverse Matrices and Their Properties 12:00
- Solving Systems Using Cramer's Rule 07:43
- Understanding Vector Spaces 08:41
- Subspaces and Span 05:50
- Linear Independence 12:56
- Basis and Dimension 10:06
- Change of Basis 09:34
- Linear Transformations on Vector Spaces 09:11
- Image and Kernel 05:35
- Orthogonality and Orthonormality 11:48
- The Gram-Schmidt Process 10:07
- Finding Eigenvalues and Eigenvectors 17:10
- Diagonalization 08:43
- Complex, Hermitian, and Unitary Matrices 09:00
- Further Matrix Decompositions: LU, Cholesky, QR, and SVD 10:10
- Introduction to Algebra: Using Variables 04:04
- Basic Number Properties for Algebra 05:16
- Algebraic Equations and Their Solutions 04:52
- Algebraic Equations With Variables on Both Sides 06:46
- Algebraic Word Problems 05:38
- Solving Algebraic Inequalities 05:43
- Square Roots, Cube Roots, and Other Roots 09:02
- Simplifying Expressions With Roots and Exponents 08:23
- Solving Algebraic Equations With Roots and Exponents 05:46
- Introduction to Polynomials 05:13
- Adding and Subtracting Polynomials 05:32
- Multiplying Binomials by the FOIL Method 06:25
- Solving Quadratics by Factoring 09:37
- Solving Quadratics by Completing the Square 07:32
- Solving Quadratics by Using the Quadratic Formula 06:55
- Solving Higher-Degree Polynomials by Synthetic Division and the Rational Roots Test 09:22
- Manipulating Rational Expressions: Simplification and Operations 09:30
- Graphing in Algebra: Ordered Pairs and the Coordinate Plane 06:56
- Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts 06:52
- 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 Lines 04:47
- Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination 10:21
- Absolute Values: Defining, Calculating, and Graphing 05:10
- What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational 09:00
- Back to Algebra: What are Functions? 07:23
- Manipulating Functions Algebraically and Evaluating Composite Functions 05:29
- Graphing Algebraic Functions: Domain and Range, Maxima and Minima 05:54
- Transforming Algebraic Functions: Shifting, Stretching, and Reflecting 07:52
- Continuous, Discontinuous, and Piecewise Functions 05:18
- Inverse Functions 06:29
- The Distance Formula: Finding the Distance Between Two Points 03:38
- Graphing Conic Sections Part 1: Circles 07:46
- Graphing Conic Sections Part 2: Ellipses 06:33
- Graphing Conic Sections Part 3: Parabolas in Standard Form 08:30
- Graphing Conic Sections Part 4: Hyperbolas 05:58
- Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros 09:15
- Graphing Rational Functions and Their Asymptotes 07:24
- Solving and Graphing Polynomial and Rational Inequalities 07:34
- Evaluating and Graphing Exponential Functions 05:59
- Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions 08:10
- Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property 06:26
- Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions 07:06
- Solving Exponential and Logarithmic Equations 07:08
- Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem 08:35
- Set Theory: Types of Sets, Unions and Intersections 06:22
- Sequences, Factorials, and Summation Notation 11:12
- Theoretical Probability, Permutations and Combinations 15:52
- Introduction to Mathematics 06:44
- Addition and Subtraction of Small Numbers 08:39
- Multiplication and Division of Small Numbers 06:20
- Understanding Fractions, Improper Fractions, and Mixed Numbers 06:13
- Large Whole Numbers: Place Values and Estimating 04:29
- Decimals: Notation and Operations 04:21
- Working With Percentages 03:36
- Converting Between Fractions, Decimals, and Percentages 05:21
- Addition and Subtraction of Large Numbers 05:57
- The Distributive Property for Arithmetic 03:19
- Multiplication of Large Numbers 06:28
- Division of Large Numbers: Long Division 05:41
- Negative Numbers 05:27
- Understanding Exponents and Their Operations 08:42
- Order of Arithmetic Operations: PEMDAS 04:22
- Divisibility, Prime Numbers, and Prime Factorization 05:54
- Least Common Multiple (LCM) 05:40
- Greatest Common Factor (GCF) 04:46
- Addition and Subtraction of Fractions 04:07
- Multiplication and Division of Fractions 05:06
- Analyzing Sets of Data: Range, Mean, Median, and Mode 05:46
- Introduction to Geometry: Ancient Greece and the Pythagoreans 04:00
- Basic Euclidean Geometry: Points, Lines, and Planes 04:19
- Types of Angles and Angle Relationships 07:24
- Types of Triangles in Euclidean Geometry 05:25
- Proving Triangle Congruence and Similarity 05:08
- Special Lines in Triangles: Bisectors, Medians, and Altitudes 06:20
- The Triangle Midsegment Theorem 03:08
- The Pythagorean Theorem 05:02
- Types of Quadrilaterals and Other Polygons 06:17
- Calculating the Perimeter of Polygons 05:08
- Circles: Radius, Diameter, Chords, Circumference, and Sectors 04:58
- Calculating the Area of Shapes 06:39
- Proving the Pythagorean Theorem 03:34
- Three-Dimensional Shapes Part 1: Types, Calculating Surface Area 07:32
- Three-Dimensional Shapes Part 2: Calculating Volume 06:17
- Introduction to Trigonometry: Angles and Radians 06:27
- Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent 07:18
- The Easiest Way to Memorize the Trigonometric Unit Circle 09:48
- Basic Trigonometric Identities: Pythagorean Identities and Cofunction Identities 05:25
- Graphing Trigonometric Functions 11:40
- Inverse Trigonometric Functions 06:54
- Verifying Trigonometric Identities 09:14
- Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-Prod 09:29
- Solving Trigonometric Equations 08:28
- The Law of Sines 05:14
- The Law of Cosines 04:38
- Polar Coordinates and Graphing Polar Equations 10:46
- Parametric Equations 04:36
- Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses 07:34
- Three-Dimensional Coordinates and the Right-Hand Rule 06:41
- Introduction to Vectors and Their Operations 10:17
- The Vector Dot Product 06:59
- Double and Triple Integrals 15:29
- Partial Derivatives and the Gradient of a Function 10:57
- Vector Fields, Divergence, and Curl 15:36
- Evaluating Line Integrals 12:54
- Green's Theorem 06:37
- Evaluating Surface Integrals 12:24
- Stokes's Theorem 08:11
- The Divergence Theorem 06:31
- Introduction to Differential Equations 04:34
- Classification of Differential Equations 07:33
- Separable First-Order Differential Equations 07:05
- Linear First-Order Differential Equations 04:46
- Exact First-Order Differential Equations 08:45
- Homogeneous Differential Equations and Bernoulli Differential Equations 10:20
- Linear Second-Order Differential Equations Part 1: Homogeneous Case 10:20
- Linear Second-Order Differential Equations Part 2: Non-Homogeneous Differential Equations 10:18
- Special Second-Order Differential Equations: Cauchy-Euler, Nonlinear, and More 09:37
- Numerical Methods for Solving Differential Equations 08:30
- Power Series Solutions Part 1: Leibniz Method 10:33
- Power Series Solutions Part 2: Frobenius Method 09:24
- Systems of Differential Equations Part 1: Modeling and Elimination 07:50
- Systems of Differential Equations Part 2: Matrices and Stability 11:50
- Laplace Transforms Part 1: Solving Differential Equations 07:58
- Laplace Transforms Part 2: Convolutions and LTI Systems 14:59
- Difference Equations and Z-Transforms 10:34
- Introduction to Partial Differential Equations: Classification and Differential Operators 10:56
- Quasi-Linear First-Order Partial Differential Equations: Lagrange’s Method 08:14
- Laplace’s Equation: Separation of Variables 11:04
- Fourier Series and Transforms Part 1: Concepts in Frequency Analysis 11:02
- Fourier Series and Transforms Part 2: Power Spectra and K-Space 06:38
- The Wave Equation Part 1: Vibrations in 1D 10:15
- The Wave Equation Part 2: Multidimensional Waves and Dispersion 08:20
- The Diffusion Equation Part 1: Separation of Variables 06:52
- The Diffusion Equation Part 2: Dimensional Analysis and Self-Similarity 10:59
- The Diffusion Equation Part 3: Green’s Functions 08:42
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