ما قبل التفاضل والتكامل | Precalculus — مقرر جامعي مجاني
مِسبار · مقرر جامعي مجاني
Precalculus
تعلم ما قبل التفاضل والتكامل (Precalculus) مجانًا عبر 10 وحدات و286 فيديو تعليميًا، بإجمالي نحو 28 ساعة، ضمن مكتبة مِسبار الجامعية.
The Precalculus course covers complex numbers; composite functions; trigonometric functions; vectors; matrices; conic sections; and probability and combinatorics. It also has two optional units on series and limits and continuity. Khan Academy's Precalculus course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
- 10 وحدات.
- 286 فيديو.
- نحو 28 ساعة مشاهدة.
- المستوى: foundation.
ابدأ مشاهدة المقرر داخل مكتبة مِسبار
التخصصات المرتبطة بالمقرر
- الهندسة الكهربائية (Electrical Engineering)
- هندسة الحاسوب (Computer Engineering)
- الهندسة الميكانيكية (Mechanical Engineering)
- الهندسة المدنية (Civil Engineering)
- الهندسة الكيميائية (Chemical Engineering)
- الهندسة الصناعية (Industrial Engineering)
- هندسة الطيران والفضاء (Aerospace Engineering)
- الذكاء الاصطناعي (Artificial Intelligence)
- علم البيانات (Data Science)
- الروبوتات (Robotics)
- الرياضيات (Mathematics)
- الإحصاء (Statistics)
- الفيزياء (Physics)
- الكيمياء (Chemistry)
- الفلك وعلوم الفضاء (Astronomy & Space Science)
- العمارة (Architecture)
- التخطيط العمراني (Urban Planning)
- تعليم الرياضيات (Mathematics Education)
وحدات ودروس المقرر
1. Composite and inverse functions
17 فيديو تعليمي.
موضوعات ودروس الوحدة
- Intro to composing functions
- Evaluating composite functions
- Evaluating composite functions: using tables
- Evaluating composite functions: using graphs
- Finding composite functions
- Evaluating composite functions (advanced)
- Modeling with composite functions
- Modeling with composite functions: skydiving
- Meaningfully composing functions
- Determining if a function is invertible
- Restricting domains of functions to make them invertible
- Reading inverse values from a graph
- Reading inverse values from a table
- Verifying inverse functions from tables
- Using specific values to test for inverses
- Verifying inverse functions by composition
- Verifying inverse functions by composition: not inverse
2. Trigonometry
37 فيديو تعليمي.
موضوعات ودروس الوحدة
- Cosine, sine and tangent of π/6 and π/3
- Trig values of π/4
- Sine & cosine identities: symmetry
- Tangent identities: symmetry
- Sine & cosine identities: periodicity
- Tangent identities: periodicity
- Intro to arcsine
- Intro to arctangent
- Intro to arccosine
- Restricting domains of functions to make them invertible
- Domain & range of inverse tangent function
- Using inverse trig functions with a calculator
- Solving for a side with the law of sines
- Solving for an angle with the law of sines
- Proof of the law of sines
- Solving for a side with the law of cosines
- Solving for an angle with the law of cosines
- Proof of the law of cosines
- Trig word problem: stars
- Solving sinusoidal equations of the form sin(x)=d
- Cosine equation algebraic solution set
- Cosine equation solution set in an interval
- Sine equation algebraic solution set
- Solving cos(θ)=1 and cos(θ)=-1
- Interpreting solutions of trigonometric equations
- Trig word problem: solving for temperature
- Trig angle addition identities
- Using the cosine angle addition identity
- Using the cosine double-angle identity
- Proof of the sine angle addition identity
- Proof of the cosine angle addition identity
- Proof of the tangent angle sum and difference identities
- Finding trig values using angle addition identities
- Using the tangent angle addition identity
- Using trig angle addition identities: finding side lengths
- Using trig angle addition identities: manipulating expressions
- Using trigonometric identities
3. Complex numbers
22 فيديو تعليمي.
موضوعات ودروس الوحدة
- Plotting numbers on the complex plane
- Distance & midpoint of complex numbers
- Intro to complex number conjugates
- Complex number conjugates
- Dividing complex numbers
- Complex numbers & sum of squares factorization
- Factoring sum of squares
- Factoring polynomials using complex numbers
- Absolute value of complex numbers
- Complex numbers with the same modulus (absolute value)
- Absolute value & angle of complex numbers
- Polar & rectangular forms of complex numbers
- Converting a complex number from polar to rectangular form
- Multiplying complex numbers graphically example: -3i
- Multiplying complex numbers graphically example: -1-i
- Multiplying complex numbers in polar form
- Dividing complex numbers in polar form
- Taking and visualizing powers of a complex number
- Complex number equations: x³=1
- The Fundamental theorem of Algebra
- Quadratics & the Fundamental Theorem of Algebra
- Number of possible real roots of a polynomial
4. Rational functions
27 فيديو تعليمي.
موضوعات ودروس الوحدة
- Reducing rational expressions to lowest terms
- End behavior of rational functions
- Discontinuities of rational functions
- Graphing rational functions according to asymptotes
- Graphs of rational functions: y-intercept
- Graphs of rational functions: horizontal asymptote
- Graphs of rational functions: vertical asymptotes
- Graphs of rational functions: zeros
- Analyzing structure word problem: pet store (1 of 2)
- Analyzing structure word problem: pet store (2 of 2)
- Combining mixtures example
- Rational equations word problem: combined rates
- Rational equations word problem: combined rates (example 2)
- Rational equations word problem: eliminating solutions
- Reasoning about unknown variables
- Reasoning about unknown variables: divisibility
- Structure in rational expression
- Multiplying & dividing rational expressions: monomials
- Multiplying rational expressions
- Dividing rational expressions
- Adding & subtracting rational expressions: like denominators
- Intro to adding rational expressions with unlike denominators
- Adding rational expression: unlike denominators
- Subtracting rational expressions: unlike denominators
- Least common multiple of polynomials
- Subtracting rational expressions: factored denominators
- Subtracting rational expressions
5. Conic sections
12 فيديو تعليمي.
موضوعات ودروس الوحدة
- Intro to conic sections
- Intro to ellipses
- Ellipse standard equation from graph
- Ellipse graph from standard equation
- Foci of an ellipse from equation
- Intro to hyperbolas
- Vertices & direction of a hyperbola
- Vertices & direction of a hyperbola (example 2)
- Graphing hyperbolas (old example)
- Foci of a hyperbola from equation
- Proof of the hyperbola foci formula
- Equation of a hyperbola not centered at the origin
6. Vectors
25 فيديو تعليمي.
موضوعات ودروس الوحدة
- Intro to vectors and scalars
- Representing quantities with vectors
- Interpreting statements about vectors
- Introduction to vector components
- Finding the components of a vector
- Comparing the components of vectors
- Vector magnitude from graph
- Vector magnitude from components
- Vector magnitude from initial & terminal points
- Scalar multiplication: component form
- Scalar multiplication: magnitude and direction
- Adding & subtracting vectors
- Adding & subtracting vectors end-to-end
- Parallelogram rule for vector addition
- Subtracting vectors end-to-end
- Subtracting vectors with parallelogram rule
- Vector addition & magnitude
- Direction of vectors from components: 1st & 2nd quadrants
- Direction of vectors from components: 3rd & 4th quadrants
- Vector components from magnitude & direction
- Vector components from magnitude & direction: word problem
- Adding vectors in magnitude and direction form
- Vector word problem: resultant velocity
- Vector word problem: hiking
- Vector word problem: resultant force
7. Matrices
35 فيديو تعليمي.
موضوعات ودروس الوحدة
- Intro to matrices
- Using matrices to represent data: Networks
- Using matrices to represent data: Payoffs
- Multiplying matrices by scalars
- Adding & subtracting matrices
- Using matrices to manipulate data: Pet store
- Using matrices to manipulate data: Game show
- Matrices as transformations of the plane
- Working with matrices as transformations of the plane
- Intro to determinant notation and computation
- Interpreting determinants in terms of area
- Finding area of figure after transformation using determinant
- Proof: Matrix determinant gives area of image of unit square under mapping
- Using matrices to transform the plane: Mapping a vector
- Using matrices to transform the plane: Composing matrices
- Using matrices to transform a 4D vector
- Composing 3x3 matrices
- Intro to matrix multiplication
- Multiplying matrices
- Defined matrix operations
- Intro to identity matrix
- Dimensions of identity matrix
- Is matrix multiplication commutative?
- Associative property of matrix multiplication
- Zero matrix & matrix multiplication
- Using properties of matrix operations
- Using identity & zero matrices
- Representing systems of equations with matrices
- Representing systems of any number of equations with matrices
- Inverse matrix introduction
- Invertible matrices and determinants
- Invertible matrices and transformations
- Inverse matrices and matrix equations
- Finding inverses of 2x2 matrices
- Solving linear systems with matrices
8. Probability and combinatorics
36 فيديو تعليمي.
موضوعات ودروس الوحدة
- Probability with Venn diagrams
- Addition rule for probability
- Compound probability of independent events
- Independent events example: test taking
- General multiplication rule example: independent events
- Dependent probability introduction
- General multiplication rule example: dependent events
- Interpreting general multiplication rule
- Factorial and counting seat arrangements
- Permutation formula
- Possible three letter words
- Zero factorial or 0!
- Ways to arrange colors
- Ways to pick officers
- Intro to combinations
- Combination formula
- Handshaking combinations
- Combination example: 9 card hands
- Probability using combinations
- Example: Lottery probability
- Example: Different ways to pick officers
- Probability with permutations & combinations example: taste testing
- Probability with combinations example: choosing groups
- Probability with combinations example: choosing cards
- Mega millions jackpot probability
- Constructing a probability distribution for random variable
- Valid discrete probability distribution examples
- Probability with discrete random variable example
- Theoretical probability distribution example: tables
- Theoretical probability distribution example: multiplication
- Probability distributions from empirical data
- Using probabilities to make fair decisions example
- Mean (expected value) of a discrete random variable
- Interpreting expected value
- Expected payoff example: lottery ticket
- Expected payoff example: protection plan
9. Series
23 فيديو تعليمي.
موضوعات ودروس الوحدة
- Geometric series introduction
- Geometric series intro
- Finite geometric series formula
- Worked examples: finite geometric series
- Geometric series word problems: swing
- Geometric series word problems: hike
- Summation notation
- Geometric series with sigma notation
- Worked example: finite geometric series (sigma notation)
- Finite geometric series word problem: social media
- Finite geometric series word problem: mortgage
- Intro to the Binomial Theorem
- Pascal's triangle and binomial expansion
- Expanding binomials
- Expanding binomials w/o Pascal's triangle
- Binomial expansion & combinatorics
- Pascal's triangle & combinatorics
- Arithmetic series intro
- Arithmetic series formula
- Worked example: arithmetic series (sigma notation)
- Worked example: arithmetic series (sum expression)
- Worked example: arithmetic series (recursive formula)
- Proof of finite arithmetic series formula
10. Limits and continuity
53 فيديو تعليمي.
موضوعات ودروس الوحدة
- Limits intro
- Estimating limit values from graphs
- Unbounded limits
- One-sided limits from graphs
- One-sided limits from graphs: asymptote
- Connecting limits and graphical behavior
- Approximating limits using tables
- Estimating limits from tables
- One-sided limits from tables
- Limit properties
- Limits of combined functions
- Limits of combined functions: piecewise functions
- Theorem for limits of composite functions
- Theorem for limits of composite functions: when conditions aren't met
- Limits of composite functions: internal limit doesn't exist
- Limits of composite functions: external limit doesn't exist
- Limits by direct substitution
- Undefined limits by direct substitution
- Limits of trigonometric functions
- Limits of piecewise functions
- Limits of piecewise functions: absolute value
- Limits by factoring
- Limits by rationalizing
- Trig limit using Pythagorean identity
- Trig limit using double angle identity
- Strategy in finding limits
- Squeeze theorem intro
- Limit of sin(x)/x as x approaches 0
- Limit of (1-cos(x))/x as x approaches 0
- Types of discontinuities
- Continuity at a point
- Worked example: Continuity at a point (graphical)
- Worked example: point where a function is continuous
- Worked example: point where a function isn't continuous
- Continuity over an interval
- Functions continuous on all real numbers
- Functions continuous at specific x-values
- Removing discontinuities (factoring)
- Removing discontinuities (rationalization)
- Introduction to infinite limits
- Infinite limits and asymptotes
- Analyzing unbounded limits: rational function
- Analyzing unbounded limits: mixed function
- Introduction to limits at infinity
- Functions with same limit at infinity
- Limits at infinity of quotients (Part 1)
- Limits at infinity of quotients (Part 2)
- Limits at infinity of quotients with square roots (odd power)
- Limits at infinity of quotients with square roots (even power)
- Intermediate value theorem
- Worked example: using the intermediate value theorem
- Justification with the intermediate value theorem: table
- Justification with the intermediate value theorem: equation
مقررات مرتبطة
- حساب المثلثات | Trigonometry
- الإحصاء والاحتمالات | Statistics & probability
- التفاضل والتكامل AP (AB) | AP®︎ Calculus AB
- التفاضل والتكامل AP (BC) | AP®︎ Calculus BC
- الإحصاء AP | AP®︎ Statistics
- التفاضل والتكامل متعدد المتغيرات | Multivariable calculus
المصدر والحقوق
المحتوى الأصلي المرخص: أكاديمية خان. تقوم مِسبار بالفهرسة والتنظيم حسب التخصص، وتعرض الفيديوهات المرخصة غير التجارية داخل مكتبة مجانية مستقلة.