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Application was developed primarily through work with a number of AP Calculus classes, so it contains what most students need to prepare for the AP Calculus Exam (AB or BC)
or a first‐year college Calculus course. In addition, a number of more advanced topics have
been added to this application to whet the student’s appetite for higher level study.
C1:Functions and Limits
Functions
Continuity Examples
Limits
Techniques for Finding Limits
Indeterminate Forms
When Limits Fail to Exist
C2:Differentiation
Definition, Basic Rules, Product Rule
Quotient, Chain and Power Rules; Exponential and Logarithmic Functions
Trigonometric and Inverse Trigonometric Functions
Generalized Product Rule
Inverse Function Rule
Partial Differentiation
Implicit Differentiation
Logarithmic Differentiation
C3:Applications of Derivatives
Maxima and Minima (i.e., Extrema)
Inflection Points
Special Case: Extrema and Inflection Points of Polynomials
Key Points on f(x), f'(x) and f''(x)
Curve Sketching
Determining the Shape of a Curve Based On Its Derivatives
Rolles's Theorem and the Mean Value Theorem (MVT)
Related Rates
Kinematics (Particle Motion)
Differentials
Curvature
Newton's Method
C4:Integration
Indefinite Integration (Antiderivatives)
Exponential and Logarithmic Functions
Trigonometric Functions
Inverse Trigonometric Functions
Selecting the Right Function for an Intergral
C5:Techniques of Integration
u ‐Substitution
Integration by Partial Fractions
Integration by Parts
Integration by Parts ‐ Tabular Method
Integration by Trigonometric Substitution
Impossible Integrals
C6:Hyperbolic Functions
Definitions
Identities
Relationship to Trigonometric Functions
Inverse Hyperbolic Functions
Graphs of Hyperbolic Functions and Their Inverses
Derivatives
Integrals
C7:Definite Integrals
Riemann Sums
Rules of Definite Integration
Fundamental Theorems of Calculus
Properties of Definite Integrals
Solving Definite Integrals with Directed Line Segments
u ‐Subsitution
Special Techniques for Evaluation
Derivative of an Integral
C8:Applications of Integration
Area Under a Curve
Area Between Curves
Area in Polar Form
Areas of Limacons
Arc Length
Comparison of Formulas for Rectangular, Polar and Parametric Forms
Area of a Surface of Revolution
Volumes of Solids of Revolution
C9:Improper Integrals
Definite Integrals with Infinite Limits of Integration
Definite Integrals with Discontinuous Integrands
C10:Differential Equations
Definitions
Separable First Order Differential Equations
Slope Fields
Logistic Function
Numerical Methods
C11:Vector Calculus
Introduction
Special Unit Vectors
Vector Components
Properties of Vectors
Dot Product
Cross Product
Triple Products
Kinematics (Particle Motion)
Gradient
Divergence
Curl
Laplacian
C12:Sequences
Definitions and Types of Sequences
More Definitions and Theorems
Limits (Convergence and Divergence)
Basic Recursive Sequence Theory
C13:Series
Introduction
Key Properties
n‐th Term Convergence Theorems
Power Series
Telescoping Series
Geometric Series
Estimating the Value of Series with Positive Terms
Riemann Zeta Function (p ‐Series)
Bernoulli Numbers
Convergence Tests
Alternating Series
Radius and Interval of Convergence of Power Series
Summary of Convergence/Divergence Tests
C14:Taylor and MacLaurin Series
Taylor Series
MacLaurin Series
LaGrange Remainder
C15:Miscellaneous Cool Stuff
e
Derivation of Euler's Formula
Logarithms of Negative Real Numbers and Complex Numbers
What Is i i
Derivative of e to a Complex Power (ez)
Derivatives of a Circle
Derivatives of a Ellipse
Derivatives of a Hyperbola
Derivative of: (x+y)3=x3+y3
Inflection Points of the PDF of the Normal Distribution
Appendices
Key Definitions
Key Theorems
List of Key Derivatives and Integrals
Key Functions and Their Derivatives
Geometry and Trigonometry Formulas
Polar and Parametric Equations
Interesting Series
Aplikasi dikembangkan terutama melalui kerja dengan sejumlah kelas Kalkulus AP, jadi ini berisi apa yang kebanyakan siswa harus siapkan untuk Ujian Kalkulus AP (AB atau BC)
atau kursus Kalkulus kuliah tahun pertama. Selain itu, sejumlah topik yang lebih maju miliki
ditambahkan ke aplikasi ini untuk membangkitkan minat siswa untuk belajar tingkat yang lebih tinggi.
C1: Fungsi dan Batasan
Fungsi
Contoh Kontinuitas
Batas
Teknik untuk Menemukan Batas
Bentuk Tidak Pasti
Ketika Batas Gagal untuk Ada
C2: Diferensiasi
Definisi, Aturan Dasar, Aturan Produk
Aturan Quotient, Rantai dan Kekuasaan; Fungsi Eksponensial dan Logaritma
Trigonometri dan Fungsi Trigonometri Invers
Aturan Produk Umum
Aturan Fungsi Terbalik
Diferensiasi parsial
Diferensiasi implisit
Diferensiasi logaritmik
C3: Aplikasi Derivatif
Maxima dan Minima (yaitu, Extrema)
Poin Infleksi
Kasus Khusus: Poin Ekstrema dan Infleksi Polinomial
Key Points pada f (x), f '(x) dan f' '(x)
Curve Sketching
Menentukan Bentuk Kurva Berbasis Derivatifnya
Teorema Rolles dan Teorema Nilai Rata-rata (MVT)
Harga Terkait
Kinematika (Partikel Motion)
Diferensial
Lengkungan
Metode Newton
C4: Integrasi
Integrasi tak terbatas (Antiderivatif)
Fungsi Eksponensial dan Logaritma
Fungsi trigonometri
Fungsi Inversi Trigonometri
Memilih Fungsi Kanan untuk suatu Intergral
C5: Teknik Integrasi
u ‐Substitusi
Integrasi dengan Fraksi Parsial
Integrasi oleh Parts
Integrasi oleh Bagian - Metode Tabular
Integrasi dengan Substitusi Trigonometri
Integral Tidak Mungkin
C6: Fungsi Hiperbolik
Definisi
Identitas
Hubungan dengan Fungsi Trigonometri
Fungsi Hiperbolik Invers
Grafik Fungsi Hiperbolik dan Inversenya
Derivatif
Integrasi
C7: Definite Integals
Riemann Sums
Aturan Integrasi Pasti
Teorema Dasar Kalkulus
Properti dari Integral Yang Pasti
Memecahkan Integral Yang Pasti dengan Segmen Baris Terarah
u ‐ Berlangganan
Teknik Khusus untuk Evaluasi
Derivatif dari Integral
C8: Aplikasi Integrasi
Area Di Bawah Kurva
Area Antara Kurva
Area dalam Polar Form
Wilayah Limacons
Panjang Busur
Perbandingan Rumus untuk Bentuk Persegi, Polar dan Parametrik
Luas Permukaan Revolusi
Volume Solid Revolusi
C9: Integral yang Tidak Pantas
Integral yang Pasti dengan Batas Integrasi Tanpa Batas
Integral Tertentu dengan Integands Terputus
C10: Persamaan Diferensial
Definisi
Persamaan Diferensial First Order Terpisah
Bidang Lereng
Fungsi Logistik
Metode Numerik
C11: Vektor Kalkulus
pengantar
Vektor Unit Khusus
Komponen Vektor
Properti dari Vektor
Produk titik
Lintas Produk
Produk Triple
Kinematika (Partikel Motion)
Gradien
Perbedaan
Ikal
Laplacian
C12: Urutan
Definisi dan Jenis Urutan
Lebih Banyak Definisi dan Teorema
Batas (Konvergensi dan Divergensi)
Teori Urutan Rekursif Dasar
C13: Seri
pengantar
Properti Kunci
Teori-teori Konvergensi Istilah ke-6
Seri Daya
Seri Telescoping
Seri Geometris
Memperkirakan Nilai Seri dengan Persyaratan Positif
Fungsi Riemann Zeta (p ‐Series)
Bernoulli Numbers
Tes Konvergensi
Seri Bolak-balik
Radius dan Interval of Convergence of Power Series
Ringkasan Pengujian Konvergensi / Divergensi
C14: Seri Taylor dan MacLaurin
Seri Taylor
MacLaurin Series
LaGrange Remainder
C15: Macam-macam Cool Stuff
e
Turunan Formula Euler
Logaritma Bilangan Real Negatif dan Bilangan Kompleks
Apa itu aku?
Derivatif e ke Kekuatan Kompleks (ez)
Derivatif Lingkaran
Derivatif dari Ellipse
Derivatif dari Hyperbola
Derivatif: (x + y) 3 = x3 + y3
Titik Infleksi PDF dari Distribusi Normal
Lampiran
Definisi Kunci
Teorema Kunci
Daftar Kunci Derivatif dan Integral
Fungsi Utama dan Derivatifnya
Rumus Geometri dan Trigonometri
Persamaan Kutub dan Parametrik
Seri yang menarik
It's very easy
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