Ace Calculus 1 In 9 Hours (the Complete Course)
 

| Duration: 9h 11m
A prerequisite for all science stream: learn the basic concepts, methods, and applications of differential calculus
What you'll learn
Find limits of functions (graphically, numerically and algebraically)
Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions
Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation
Identify limits of indeterminate type and solve them using L'Hôpital's rule or other techniques
Understand the relationship between derivatives and rates of change
Verify a general or particular solution to a differential equation
Estimate using linear approximation
Use derivatives to study the characteristics of curves and construct detailed graphs of nontrivial functions using derivatives and limits
Solve optimization problems
Requirements
Precalculus (algebra, trigonometry, and functions)
Description
HOW THIS COURSE WORK:This course, Ace Calculus 1 in 9 Hours (The Complete Course), has everything you need to know for Calculus 1, including video and notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and derivations of rules and theorems. The course is organized into the following sections:Review: PrecalculusLimits and ContinuityDifferentiationDerivatives of Transcendental FunctionsLimits - Indeterminate FormsApplications of DifferentiationCONTENT YOU WILL GET INSIDE EACH SECTION:Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.Notes: In this section, you will find my notes that I wrote during lecture. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).Extra notes: I provide some extra notes, including formula sheets and some other useful study guidance.Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.THINGS THAT ARE INCLUDED IN THE COURSE:An instructor who truly cares about your successLifetime access to Ace Calculus 1 in 9 Hours (The Complete Course)Friendly support in the Q&A sectionUdemy Certificate of Completion available for downloadBONUS #1: Downloadable lectures so you can watch whenever and wherever you are.BONUS #2: Downloadable lecture notes and some extra notes (i.e. formula sheet) so you can review the lectures without having a device to watch/listen.BONUS #3: A review section on precalculus, including algebra, graphing, asymptotes, composition functions, and inverse functions.BONUS #4: Nine assignments with solutions for Calculus 1 in total that make you productive while taking the course.BONUS #5: Step-by-step guide to help you solve problems.See you inside!- Gina :)
Overview
Section 1: Introduction
Lecture 1 Overview
Lecture 2 Welcome and How It Works
Lecture 3 Tips to Maximize Your Learning
Section 2: Precalculus Review
Lecture 4 Downloadable Notes
Lecture 5 Algebra
Lecture 6 Functions: Graphing
Lecture 7 Functions: Domain and Range
Lecture 8 Functions: Asymptotes
Lecture 9 Functions: Composition Functions
Lecture 10 Functions: Inverse Functions
Section 3: Limits and Continuity
Lecture 11 Downloadable Notes
Lecture 12 Introduction to Limits
Lecture 13 Techniques of Limits
Lecture 14 Rules of Limits
Lecture 15 One-sided Limits
Lecture 16 Infinite Limits and Vertical Asymptotes
Lecture 17 Limits at Infinity and Horizontal Asymptotes
Lecture 18 Limits of Trigonometric Functions
Lecture 19 Squeeze Theorem
Lecture 20 Definition of Continuity
Lecture 21 Examples: Continuity
Lecture 22 Polynomials and Continuity
Lecture 23 Left- and Right-Continuity
Lecture 24 Examples: Limit and Continuity on Graph
Lecture 25 Continuous on an Interval
Lecture 26 Intermediate Value Theorem (IVT)
Section 4: Differentiation
Lecture 27 Downloadable Notes
Lecture 28 Secant and Tangent Lines
Lecture 29 Definition of Derivative Function
Lecture 30 Power Rule
Lecture 31 Derivative Notation
Lecture 32 Constant Multiple Rule
Lecture 33 Sum and Difference Rules
Lecture 34 Product Rule
Lecture 35 Quotient Rule
Lecture 36 Differentiability
Lecture 37 Normal Line
Lecture 38 Higher Order Derivatives
Lecture 39 Chain Rule
Lecture 40 Implicit Differentiation
Lecture 41 Example: Implicit Differentiation
Section 5: Derivatives of Transcendental Functions
Lecture 42 Downloadable Notes
Lecture 43 Review on Trigonometric Functions
Lecture 44 Derivatives of Trigonometric Functions
Lecture 45 Examples: Derivatives of Trigonometric Functions
Lecture 46 Inverse Trigonometric Functions
Lecture 47 Derivatives of Inverse Trigonometric Functions
Lecture 48 Review on Exponential and Log Rules
Lecture 49 Derivatives of Exponential and Log Functions
Lecture 50 Log Differentiation
Lecture 51 Examples: Log Differentiation
Section 6: Limits - Indeterminate Forms
Lecture 52 Downloadable Notes
Lecture 53 L'Hôpital's Rule
Lecture 54 More Indeterminate Type
Section 7: Applications: Rates of Change
Lecture 55 Downloadable Notes
Lecture 56 Rates of Change
Lecture 57 Examples: Rectilinear Motion
Lecture 58 Calculus in Physics (Kinematic Equations)
Section 8: Applications: Differential Equations
Lecture 59 Downloadable Notes
Lecture 60 Introduction to Differential Equations
Lecture 61 Simple Harmonic Motion
Lecture 62 Example: Simple Harmonic Motion
Section 9: Applications: Mean Value Theorem
Lecture 63 Downloadable Notes
Lecture 64 Mean Value Theorem (MVT)
Lecture 65 Rolle's Theorem (Special Case of MVT)
Section 10: Applications: Linear Approximation
Lecture 66 Downloadable Notes
Lecture 67 Differentials
Lecture 68 Examples: Estimation
Section 11: Applications: Curve Sketching
Lecture 69 Downloadable Notes
Lecture 70 Orthogonality
Lecture 71 Increasing and Decreasing
Lecture 72 Local Max/Min and Critical Points
Lecture 73 Examples: Critical Values
Lecture 74 First Derivative Test
Lecture 75 Concavity and Inflection Points
Lecture 76 Second Derivative Test
Lecture 77 Extreme Value Theorem (EVT)
Lecture 78 Curve Sketching
Lecture 79 Example 1: Curve Sketching
Lecture 80 Example 2: Curve Sketching
Section 12: Applications: Optimization Problems
Lecture 81 Downloadable Notes
Lecture 82 Optimization Problems
Lecture 83 Examples: Optimization Problems
Section 13: Conclusion
Lecture 84 Thank You & Good Luck & Next Step
Lecture 85 BONUS: Let's Keep Learning!
Anyone who has completed precalculus (algebra and trigonometry) and wants to learn some more advanced math,Current calculus 1 students who are looking for extra help outside school,Anyone who is not in science stream but wants to study calculus for fun