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所在平台: Udemy |
课程主页: https://www.udemy.com/course/computer-oriented-numerical-techniques/
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Coursera 课程《计算机数值技术》(BCS-054) 课程总结 本课程《计算机数值技术》(BCS-054) 是数学的一个分支——数值分析，旨在开发、分析和评估构建性的数值解。本课程专为 BCA/MCA/(B-Tech 计算机科学) 等专业的学生设计，涵盖了解决数值方法相关问题的技巧，帮助学生在期末考试中取得优异成绩。 课程强调了计算机在数值问题求解中的作用，以及在求解过程中需要注意的误差分析。内容涵盖了以下主要主题： * **线性代数方程的数值解法：** 高斯消元法 (包括部分选主法)、雅可比迭代法、高斯-赛德尔迭代法。 * **非线性方程的数值解法：** 二分法、假位法、割线法、牛顿-拉夫逊法。 * **算子：** 前向算子、后向算子、移位算子、中央差分算子，以及它们与移位算子的关系。 * **等距插值：** 牛顿前向插值法、牛顿后向插值法。 * **不等距插值：** 拉格朗日插值法、分差插值法。 * **数值积分方法：** 梯形法则、辛普森法则。 * **初值问题：** 欧拉法、龙格-库塔法。 * **数值微分：** 牛顿前向法、牛顿后向法、拉格朗日法。 * **计算机算术：** 误差 (绝对误差、相对误差、百分比误差)、浮点数表示、浮点数运算、泰勒/麦克劳林级数问题等。 本课程通过介绍一系列经典的数值方法及其问题和解决方案，帮助学生理解计算机导向的数值分析，并为他们在计算机科学领域的研究和实践打下坚实的基础。
Numerical Analysis is a branch of mathematics that helps to develop, analysis and evaluation of constructive numerical solutions This course has been designed to solve numerical methods related questions so that student pursuing their BCA/MCA/(B-Tech computer Science) can achieve best in semester exams. Numerical Analysis has become essentially the discipline of computer Oriented Numerical Analysis. For solving numerical problems, the use of computer puts restrictions on the solution process. so for solving problem there must be careful analysis with respect to quantum of possible error. However, this course has been restricted to discussing some well known methods and their problems along with solutions. This course would include various topics like Linear Algebraic Equations (Gauss Elimination method, Partial Pivoting Methods, Gauss Jacobi method, Gauss Seidel Method), Non-Linear Equations ( Bisection method, Regula-Falsi Method, Secant Method, Newton Raphson Method), Operators(Forward Operator, Backward Operator, Shift Operator, Central Difference Operator, Averaging Operator and their relationships with Shift operators), Interpolation with equal intervals( Newton Forward Method, Newton Backward Method), Interpolation with unequal intervals (Lagrange's Method, Divided Difference Method), Method of Integration (Trapezoidal Rule, Simpson's Rule), Initial Value Problem ( Euler's Method , Runge Kutta Method), Numerical Differentiation( Newton Forward, Newton Backward, Lagrange's method) and Computer Arithmetic ( Error, Absolute Error, Relative Error, Percentage Error, Floating Point Representation, Floating Number Operations, Taylor/Maclaurin Series questions etc..
