MATH 241 • Tüm Sınavlar • Engineering Mathematics I
İhsan Doğramacı Bilkent Üniversitesi MATH 241 (Engineering Mathematics I) Midterm sınavına hazırlık paketi.
İşlenen konular: Complex Numbers, Systems of Linear Equations, Matrix Operations and Inverse, Matrix Equations, Elementary Matrices, Determinants, Cramer's Rule, Vectors: Linear Combination and Span, Linear Independence, Vector Spaces and Subspaces, Basis for Subspaces: Row and Column Spaces.
Eğitmenler
Dorukhan Özcan
Co-Founder & CEO
Unicourse şirketinin kurucu ortağıyım. 2016 senesinde Galatasaray Lisesinden mezun oldum. Geçtiğimiz dört sene içerisinde 2000 saatten fazla ders anlattım. Anlattığım dersler sırasıyla; Calculus, Çok değişkenli Calculus, Lineer Cebir, Differansiyel Denklemler, Uygulamalı İstatistik ve Stokastik Modelleme dersleridir. Doping Hafıza şirketinde 2017 - 2022 seneleri arasında CEO danışmanlığı yaptım. Koç Üniversitesi Endüstri Mühendisliği ve Ekonomi çift anadal programını tam burslu olarak, 3.96/4.00 not ortalamasıyla bitirdim. Kadıköy Modalıyım.
Tolga Temiz
Eğitmen
2016 senesinde başladığım Koç Üniversitesi Matematik bölümünden 2020 senesinde fakülte üçüncüsü olarak mezun oldum. Lisans ve yüksek lisans eğitimlerim boyunca çeşitli derslerde asistanlık yaptım. 2021'de Koç Üniversitesi'nde Matematik yüksek lisansına başladım ve 2023 yılında mezun oldum. Şimdi Michigan State Üniversitesi'nde doktora yapıyorum. Topoloji alanıyla ilgilenmekteyim.
Konular
Complex Numbers
8 konu anlatımı
Complex Numbers - 1
Complex Numbers - 2
Complex Numbers - 3
Polar Representation - 1
Polar Representation - 2
Polar Representation - 3
De Moivre's Theorem - 1
De Moivre's Theorem - 2
Systems of Linear Equations
4 konu anlatımı · 3 soru
Augmented Matrix - Row Operations 1
Augmented Matrix - Row Operations 2
Existence and Uniqueness of Solution
Free Variables
Exam-like Questions 1
Exam-like Questions 2
Exam like Question 3
Matrix Operations and Inverse
3 konu anlatımı · 3 soru
Fundamental Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
Exam-like Question 1
Exam-like Question 2
Exam like Question 3
Matrix Equations
2 konu anlatımı · 3 soru
Matrix Equation
Solving AX = B with Inverse
Exam like Question 1
Exam-like Question 2
Exam like Question 3
Elementary Matrices
2 konu anlatımı · 3 soru
Elementary Matrix
Inverse of Elementary Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Determinants
5 konu anlatımı · 3 soru
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant
Properties of Determinant 2
Adjoint Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Cramer's Rule
2 konu anlatımı · 1 soru
Cramer's Rule I
Cramer's Rule II
Exam like Question 1
Vectors: Linear Combination and Span
7 konu anlatımı · 3 soru
Vector Properties
Linear Combination 1
Linear Combination 2
Formal Definition of Linear Combination
Span of Vectors 1
Span of Vectors 2
Solutions of Homogeneous Linear Systems
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Linear Independence
3 konu anlatımı · 3 soru
Linear Independent Sets
Linear Independence of Matrices
Special Theorem for Matrix Equation
Exam-like Questions 1
Exam-like Questions 2
Exam-like Question 3
Vector Spaces and Subspaces
3 konu anlatımı · 7 soru
Vector Spaces and Subspaces
Polynomial Subspaces
Matrix Spaces & Matrix Subspaces
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Basis for Subspaces: Row and Column Spaces
6 konu anlatımı · 4 soru
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Basis for Polynomial Subspaces 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
General Review Problems
19 soru
Existence and Uniqueness
Determinant and Invertibility
Properties of Determinants
Subspace or not 1
Subspace or not 2
Subspaces or not 3
Basis for Subspaces 1
Basis for Subspaces 2
Basis for Subspaces 3
Basis for Subspaces 4
Polynomials Basis 1
Polynomials Basis 2
Polynomials Basis 3
Polynomials Basis 4
Null & Column & Row Spaces
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3
Theory Problem 1
Theory Problem 2
Orthogonality, Orthogonal Complement and Basis
4 konu anlatımı · 4 soru
Key concepts for orthogonality
Orthogonal Complement
Orthagonal Complement 2
Orthogonal Sets and Basis
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam like Question 4
The Gram-Schmidt Process
2 konu anlatımı · 4 soru
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Angle Between Vectors for a Given Inner Product
Eigenvalues and Eigenvectors
7 konu anlatımı
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Algebraic and Geometric Multiplicities
Eigenspace of Matrices
Complex Eigenvalues
Complex Eigenvalues 2
Diagonalization of Matrices
2 konu anlatımı · 4 soru
Diagonalization 1
Diagonalization 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Cayley Hamilton Theorem
1 konu anlatımı · 2 soru
Cayley-Hamilton Theorem
Application of Cayley-Hamilton Theorem
Application of Cayley-Hamilton Theorem
Linear Homogeneous DEs with Constant Coefficients
2 konu anlatımı · 5 soru
General Theory of nth Order DEs (Wronskian)
Homogeneous DEs with Constant Coefficients
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Z-Transform
4 konu anlatımı · 2 soru
Introduction
Properties of Z-Transform
Example 1
Example 2
Exam-like Question 1
Exam-like Question 2
The Laplace Transform
6 konu anlatımı · 3 soru
The Laplace Transform 1
The Laplace Transform 2
The Laplace Transform 3
The Laplace Transform 4
Inverse Laplace Transform 1
Inverse Laplace Transform 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Solving Differential Equations by Laplace Transform
3 konu anlatımı · 3 soru
Laplace Transform of Derivative
Laplace Transform and Initial Value Problems 1
Laplace Transform and Initial Value Problems 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Systems of First Order Linear Equations
7 konu anlatımı · 3 soru
Introduction
Homogeneous Systems: Distinct Real Eigenvalues 1
Homogeneous Systems: Distinct Real Eigenvalues 2
Homogeneous Systems: Complex Eigenvalues 1
Homogeneous Systems: Complex Eigenvalues 2
Homogeneous Systems: Repeated Eigenvalues 1
Homogeneous Systems: Repeated Eigenvalues 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Nonhomogeneous Systems
2 konu anlatımı · 1 soru
Linear Algebra: Nonhomogeneous Systems
Non-hom. Systems: Given Particular Solution
Exam like Question