Ludium - Learn by Doing

Calculus 1

01Slope Formula and Point-Slope Form 02Slope-Intercept Form (y = mx + b)03Parallel & Perpendicular Lines 04Slope, Tangent, and the Distance Formula Problem set0/10 Problem set 20/10 Practice∞

01Functions, Notation, and the Vertical Line Test 02Piecewise Functions and Absolute Value 03Domain of Functions 04Holes vs Vertical Asymptotes and Finding Range 05Even and Odd Functions Problem set0/10 Problem set 20/10 Practice∞

01Angles in Radians and Degrees 02The Unit Circle and All Six Trig Functions 03Reference Angles and ASTC 04Amplitude, Period, and Phase Shifts Problem set0/10 Problem set 20/10 Practice∞

01Arithmetic Operations on Functions 02Function Composition: f(g(x))03Decomposing Composite Functions Problem set0/10 Problem set 20/10 Practice∞

01The Two Problems That Created Calculus 02The Tangent Problem 03What Is a Limit?04Limits and the Tangent Line to y = x² 05One-Sided Limits and Vertical Asymptotes Problem set0/10 Problem set 20/10 Practice∞

01Fundamental Limit Laws 02Direct Substitution for Limits 03Indeterminate Forms: Factoring & Rationalizing 04Piecewise Function Limits 05Limits of Trigonometric Functions 06The Three Essential Trig Limits Problem set0/10 Problem set 20/10 Practice∞

01Continuity at a Point 02Types of Discontinuities 03Continuity on Intervals 04Continuity of Polynomials and Rational Functions 05The Intermediate Value Theorem Problem set0/10 Problem set 20/10 Practice∞

01The Limit Definition of the Derivative 02Computing Tangent Lines via Limits 03The General Derivative of √x 04Instantaneous Velocity Problem set0/10 Problem set 20/10 Practice∞

01The Derivative 02Polynomial Derivatives by Definition 03Derivative of √x 04Instantaneous Velocity 05Continuity vs. Differentiability Problem set0/10 Problem set 20/10 Practice∞

01The Power Rule 02Power Rule for Negative & Fractional Exponents 03Differentiating Polynomials Term by Term 04Horizontal Tangent Lines 05Higher Order Derivatives and Linearity Problem set0/10 Problem set 20/10 Practice∞

01The Product Rule 02Applying the Product Rule 03The Quotient Rule 04Nesting Product and Quotient Rules Problem set0/10 Problem set 20/10 Practice∞

01Finding Peak Sales with the Quotient Rule 02From Position to Jerk 03Finding Maximum Height with Derivatives 04Marginal Cost Problem set0/10 Problem set 20/10 Practice∞

01Proving d/dx[sin(x)] = cos(x)02The Six Trigonometric Derivatives 03Product & Quotient Rules for Trig Functions 04Trig Derivatives and Spring Motion Problem set0/10 Problem set 20/10 Practice∞

01The Chain Rule 02Combining Product and Chain Rules 03The General Power Rule 04Chain Rule with Trig Functions 05Multi-Layer Chain Rule Problem set0/10 Problem set 20/10 Practice∞

01Implicit and Explicit Functions 02Implicit Differentiation 03Implicit Products and Second Derivatives 04Tangent Lines by Implicit Differentiation Problem set0/10 Problem set 20/10 Practice∞

01Related Rates 02The Four-Step Related Rates Method 03Related Rates: The Expanding Circle 04Related Rates: Angle of Elevation Problem set0/10 Problem set 20/10 Practice∞

01Increasing and Decreasing Intervals 02Concavity and Inflection Points 03The First Derivative Test 04The Closed Interval Method Problem set0/10 Problem set 20/10 Practice∞

01Rolle's Theorem and the Mean Value Theorem 02The First Derivative Test 03Concavity and Inflection Points 04Curve Sketching with f' and f''Problem set0/10 Problem set 20/10 Practice∞

01Holes and Vertical Asymptotes 02Sign Analysis at Vertical Asymptotes 03Limits at Infinity 04Rational Function Limits at Infinity 05√(x²) = |x| and Limits at Infinity Problem set0/10 Problem set 20/10 Practice∞

01Curve Sketching in 7 Steps 02Polynomial Curve Sketching 03Analyzing Rational Functions 04Curve Sketching: f(x) = (x²−1)/x³ 05Graphing (2x²−8)/(x²−16)Problem set0/10 Problem set 20/10 Practice∞

01The 8-Step Optimization Method 02Constrained Optimization: Fence Problem 03The Closed Interval Method 04Minimizing Cylinder Surface Area Problem set0/10 Problem set 20/10 Practice∞

01Approximating Area with Rectangles 02Anti-Derivatives and Area 03Antiderivatives and the Power Rule 04Trig Integrals and Integration Properties 05Solving Initial Value Problems 06Deriving the Projectile Motion Equation Problem set0/10 Problem set 20/10 Practice∞

01U-Substitution 02U-Substitution Practice Problems 03Linearity of Integration 04Fixing U-Substitution Mismatches Problem set0/10 Problem set 20/10 Practice∞

01Sigma Notation and Summation Formulas 02Riemann Sums and the Definite Integral 03From Riemann Sums to the Definite Integral 04Evaluating Riemann Sums Problem set0/10 Problem set 20/10 Practice∞

01The Definite Integral 02Definite Integrals as Geometric Areas 03Properties of Definite Integrals 04Solving Integrals with Geometry Problem set0/10 Problem set 20/10 Practice∞

01Definite Integrals via F(b) − F(a)02Reversed Bounds and FTC Continuity 03Net Signed Area vs. Total Area 04Fundamental Theorem of Calculus, Part 1 05U-Substitution with Definite Integrals 06Even and Odd Functions in Integration Problem set0/10 Problem set 20/10 Practice∞

01Area Between Two Curves 02Area Between Two Curves 03Area Between Curves That Cross 04Integrating with Respect to Y Problem set0/10 Problem set 20/10 Practice∞

01Volume by Slicing 02The Disc Method 03The Washer Method 04Disc and Washer Method Around the Y-Axis 05Washer Method with Non-Axis Revolution Problem set0/10 Problem set 20/10 Practice∞

01Method of Cylindrical Shells 02Shells vs. Washers: Choosing the Variable 03Cylindrical Shells Around the Y-Axis 04Cylindrical Shells Around the X-Axis Problem set0/10 Problem set 20/10 Practice∞

01Deriving the Arc Length Formula 02Arc Length: Perfect Squares & U-Substitution 03Surface Area of Revolution 04Surface Area of Revolution: U-Substitution Problem set0/10 Problem set 20/10 Practice∞