Calculus 1 - Discussion of the Chain Rule for Derivatives of Functions
Comprehensive exploration of the Chain Rule, its applications, and problem-solving techniques for complex derivative calculations in calculus.
Calculus 1 - Slope of a Curve, Velocity, and Rates of Change
Explore slope of curves, velocity, and rates of change in calculus. Learn fundamental concepts for understanding derivatives and their applications in real-world scenarios.
Calculus 1 - Continuity of Functions
Explore the concept of continuity in functions, its importance in calculus, and how to determine if a function is continuous at a point or over an interval.
Calculus 1 - Properties of Limits - Techniques of Limit Computation
Explore properties of limits and master techniques for limit computation in this comprehensive lecture on fundamental calculus concepts.
Calculus 1 - Introduction to Functions
Comprehensive exploration of function concepts, including domain, range, and graphing, providing a solid foundation for calculus studies.
Vector Fields, Divergence, and Curl
Explore vector fields, divergence, and curl in mathematics. Learn about the del operator and its applications with dot and cross products to analyze vector field properties.
Double and Triple Integrals
Explore double and triple integrals, building on single integral knowledge. Learn to set up integration bounds and choose variable order through rules and examples.
Advanced Strategy for Integration in Calculus
Master advanced integration techniques in calculus, including substitution, integration by parts, and trigonometric substitution. Learn strategies for evaluating complex integrals through guided examples.
Oxford Calculus - Taylor's Theorem Explained with Examples and Derivation
Comprehensive explanation of Taylor's Theorem, including derivation and practical examples. Covers polynomial approximation of functions, Cauchy's Mean Value Theorem, and power series expansion, with interactive exercises and additional resources.
Oxford Calculus - Solving Homogeneous First Order Differential Equations
Learn to solve homogeneous first order differential equations with Oxford mathematician Dr Tom Crawford. Includes worked examples, partial fractions, implicit differentiation, and practice exercises.
Oxford Calculus - Integrating Factors Explained
Learn to solve first order linear differential equations using integrating factors. Understand the technique's derivation, application, and practice with a provided worksheet and example problems.
Oxford Calculus - Classifying 2D Critical Points Using the Discriminant
Learn to classify 2D critical points using the discriminant method. Explore maximum, minimum, and saddle points with visualizations and step-by-step derivations for multivariable functions.
Graphs of Exponential Functions - Precalculus - College Algebra
Explore exponential function graphs, understanding their unique shapes, key points, and asymptotes for a deeper grasp of this fundamental mathematical concept.
Stability of Critical Points - Differential Equations
Explore critical points in differential equations to determine solution behavior, enhancing your understanding of stability and general solution characteristics.
Using Partial Fractions in Differential Equations
Learn to apply partial fractions in solving differential equations, focusing on separation of variables techniques. Enhance your problem-solving skills in advanced calculus.
Exponent Rules - Power Rules
Learn to apply power rules for exponents, enhancing your algebraic skills and problem-solving abilities in mathematics.
Exponent Rules - Product Rule
Learn to apply the Product Rule for exponents, mastering its use in algebraic expressions and equations for more efficient problem-solving in mathematics.
The Truth About 1+2+3+...=-1/12
Explores the controversial sum 1+2+3+...=-1/12, explaining mathematical concepts behind it, addressing misconceptions, and connecting it to the Riemann zeta function and Ramanujan's work.
Ramanujan - Making Sense of 1+2+3+... = -1/12 and Co.
Explore the mathematical paradox of infinite sums equaling unexpected values, delving into Ramanujan's work, summation rules, and connections to the Riemann Zeta function.
R. Kashaev - The Connection Between Integrals and Fourier Series
Explore the intricate relationship between integrals and Fourier series, delving into mathematical concepts that bridge these fundamental analytical tools in advanced calculus and mathematical physics.
Long Time Behaviour of 2D Spherical Ideal Hydrodynamics
Explore 2D spherical ideal hydrodynamics, focusing on new discretization schemes, geometric preservation, and long-time behavior linked to point vortex dynamics.