【极致中配】预备微积分 - 大学代数/三角学 Precalculus - College Algebra/Trigonometry
系统讲解大学预备数学:函数及其性质、二次/多项式/有理/指数对数函数、数列与归纳法,以及弧度制、单位圆、三角函数与极坐标。
- 难度
- 难度 2/5 — 面向零基础到大一学生的预备内容,循序渐进,需初等代数基础
- 适合人群
- 准备学习微积分的高中生与大一新生,或需补足代数三角基础的自学者
- 前置要求
- 初中代数(会解一元一次方程、因式分解)、基础几何(了解直角三角形、坐标系)
- 课程规模
- 91 讲 · 3940播放
主题覆盖
函数与定义域函数图像变换二次方程与不等式多项式函数有理函数与渐近线指数与对数数列与数学归纳法弧度制与单位圆三角函数图像反三角函数直角三角形三角学极坐标
课程大纲(91 讲)
- P1 · Intro to Precalculus (Precalculus - College Algebra 1)3 分钟
- P2 · Introduction to Functions (Precalculus - College Algebra 2)38 分钟
- P3 · How to Evaluate Functions (Precalculus - College Algebra 3)50 分钟
- P4 · Finding the Domain of Functions (Precalculus - College Algebra 4)39 分钟
- P5 · Operations of Functions (Precalculus - College Algebra 5)21 分钟
- P6 · Using the Vertical Line Test (Precalculus - College Algebra 6)11 分钟
- P7 · Features of Graphs, Domain, Range (Precalculus - College Algebra 7)46 分钟
- P8 · Properties of Functions - Even vs Odd (Precalculus - College Algebra 8)29 分钟
- P9 · Properties of Functions - Increasing vs Decreasing (Precalculus - College Algebr14 分钟
- P10 · Properties of Functions - Extrema (Precalculus - College Algebra 10)26 分钟
- P11 · Average Rate of Change of a Function (Precalculus - College Algebra 11)10 分钟
- P12 · How to Graph Piecewise Functions (Precalculus - College Algebra 12)44 分钟
- P13 · Graphs You Must Know (Precalculus - College Algebra 13)19 分钟
- P14 · Introduction to Graph Transformations (Precalculus - College Algebra 14)46 分钟
- P15 · How to Graph with Transformations (Precalculus - College Algebra 15)31 分钟
- P16 · Introduction to Solving Quadratics (Precalculus - College Algebra 16)11 分钟
- P17 · The Square Root Method in Solving Quadratics (Precalculus - College Algebra 17)43 分钟
- P18 · Using Factoring to Solve Quadratics (Precalculus - College Algebra 18)55 分钟
- P19 · Completing the Square Made Easy (Precalculus - College Algebra 19)66 分钟
- P20 · Proving the Quadratic Formula - Twice (Precalculus - College Algebra 20)18 分钟
- P21 · Using the Quadratic Formula (Precalculus - College Algebra 21)43 分钟
- P22 · Finding Intersections of Functions (Precaluclus - College Algebra 22)18 分钟
- P23 · Using Substitutions to Solve Equations (Precalculus - College Algebra 23)46 分钟
- P24 · Graphing Quadratic Functions (Precalculus - College Algebra 24)54 分钟
- P25 · Solving Quadratic Inequalities (Precalculus - College Algebra 25)35 分钟
- P26 · Applications of Quadratic Functions (Precalculus - College Algebra 26)22 分钟
- P27 · Introduction to Polynomial Functions (Precalculus - College Algebra 27)34 分钟
- P28 · Power Functions (Precalculus - College Algebra 28)31 分钟
- P29 · Multiplicity and End Behavior of Polynomials (Precalculus - College Algebra 29)35 分钟
- P30 · Creating Polynomials from Real Zeros (Precalculus - College Algebra 30)56 分钟
- P31 · How to Sketch Polynomial Functions (Precalculus - College Algebra 31)61 分钟
- P32 · Synthetic Division and Long Division of Polynomials (Precalculus - College Algeb49 分钟
- P33 · Descartes Rule of Signs (Precalculus - College Algebra 33)31 分钟
- P34 · How to Use the Rational Zeros Theorem (Precalculus - College Algebra 34)81 分钟
- P35 · Introduction to Complex Solutions of Polynomials (Precalculus - College algebra16 分钟
- P36 · Creating Polynomials from Complex Solutions (Precalculus - College Algebra 36)40 分钟
- P37 · Finding ALL Solutions of Polynomials (Precalculus - College Algebra 37)67 分钟
- P38 · Finding Vertical Asymptotes of Rational Functions (Precalculus - College Algebra39 分钟
- P39 · Graphing Rational Functions with Transformations (Precalculus - College Algebra45 分钟
- P40 · Finding a Horizontal Asymptote of a Rational Function (Precalculus - College Alg29 分钟
- P41 · Finding an Oblique Asymptote of a Rational Function (Precalculus - College Algeb15 分钟
- P42 · Finding End Behavior of Rational Functions (Precalculus - College Algebra 42)7 分钟
- P43 · Finding Asymptotes and Holes of Rational Functions (Precalculus - College Algebr50 分钟
- P44 · Graphing Rational Functions (Precalculus - College Algebra 44)102 分钟
- P45 · Inequalities with Functions - Graphically (Precalculus - College Algebra 45)20 分钟
- P46 · Inequalities with Polynomial Functions (Precalculus - College Algebra 46)31 分钟
- P47 · Inequalities with Rational Functions (Precalculus - College Algebra 47)56 分钟
- P48 · Composition of Functions (Precalculus - College Algebra 48)28 分钟
- P49 · Finding Domain of Composite Functions (Precalculus - College Algebra 49)29 分钟
- P50 · One to One Functions (Precalculus - College Algebra 50)14 分钟
- P51 · Finding Inverse Functions (Precalculus - College Algebra 51)52 分钟
- P52 · Graphs of Exponential Functions (Precalculus - College Algebra 52)22 分钟
- P53 · Graphing Exponential Functions with Transformations (Precalculus -College Algebr35 分钟
- P54 · Solving Exponential Equations with Common Bases (Precalculus - College Algebra 536 分钟
- P55 · Introduction to Logarithms and Their Graphs (Precalculus - College Algebra 55)58 分钟
- P56 · How to Combine Logarithms (Precalculus - College Algebra 60)23 分钟
- P57 · Solving Logarithms with Common Bases (Precalculus - College Algebra 62)31 分钟
- P58 · Solving Logarithmic Equations with Exponentials (Precalculus - College Algebra 656 分钟
- P59 · Solving Exponential Equations with Logarithms (Precalculus - College Algebra 64)59 分钟
- P60 · Review of Compound Interest (Precalculus - College Algebra 65)42 分钟
- P61 · Exponential Growth and Decay (Precalculus - College Algebra 66)45 分钟
- P62 · Introduction to Sequences (Precalculus - College Algebra 67)51 分钟
- P63 · Arithmetic Sequences (Precalculus - College Algebra 69)18 分钟
- P64 · Arithmetic Series (Precalculus - College Algebra 70)13 分钟
- P65 · Geometric Sequences (Precalculus - College Algebra 71)26 分钟
- P66 · Geometric Series (Precalculus - College Algebra 72)41 分钟
- P67 · Proof by Mathematical Induction (Precalculus - College Algebra 73)21 分钟
- P68 · Introduction to Angles (Precalculus - Trigonometry 1)24 分钟
- P69 · Converting Degrees, Minutes, and Seconds (Precalculus - Trigonometry 2)16 分钟
- P70 · Introduction to Radians (Precalculus - Trigonometry 3)15 分钟
- P71 · Converting Radians and Degrees (Precalculus - Trigonometry 4)34 分钟
- P72 · Area of a Sector, Angular Velocity, Applications (Precalculus - Trigonometry 5)32 分钟
- P73 · Trigonometric Functions and the Unit Circle (Precalculus - Trigonometry 6)40 分钟
- P74 · How to Use the Unit Circle in Trigonometry (Precalculus - Trigonometry 7)41 分钟
- P75 · Basic Properties of Trigonometric Functions (Precalculus - Trigonometry 8)67 分钟
- P76 · Reciprocal Identities in Trigonometry (Precalculus - Trigonometry 9)42 分钟
- P77 · Pythagorean Identities for Trigonometric Functions (Precalculus - Trigonometry 135 分钟
- P78 · The Graphs of Sine and Cosine (Precalculus - Trigonometry 11)34 分钟
- P79 · Graphing Transformations with Sine and Cosine (Precalculus - Trigonometry 12)66 分钟
- P80 · How to Graph Phase Shifts of Trigonometric Functions (Precalculus - Trigonometry38 分钟
- P81 · Introduction to Inverse Trigonometric Functions (Precalculus - Trigonometry 17)32 分钟
- P82 · How to Use Inverse Trigonometric Functions (Precalculus - Trigonometry 18)57 分钟
- P83 · How to Find Inverse Trigonometric Functions (Precalculus - Trigonometry 19)34 分钟
- P84 · An Indepth Look at Using Inverse Trig Functions (Precalculus - Trigonometry 21)76 分钟
- P85 · Introduction to Right Triangle Trigonometry (Precalculus - Trigonometry 30)55 分钟
- P86 · Finding Sides and Angles with Right Triangle Trigonometry (Precalculus - Trigono39 分钟
- P87 · How to Convert From Rectangular Coordinates to Polar Coordinates (Precalculus -42 分钟
- P88 · How to Convert From Rectangular Equations to Polar Equations (Precalculus - Trig25 分钟
- P89 · How to Convert From Polar Equations to Rectangular Equations (Precalculus - Trig22 分钟
- P90 · How to Graph Basic Polar Equations (Precalculus - Trigonometry 41)23 分钟
- P91 · How to Graph Advanced Polar Equations with Symmetry (Precalculus - Trigonometry41 分钟
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