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陸游古詩「臥春」之意境

陸游古詩「臥春」之意境. 鄉音濃重的國文老師，為學生們朗讀一首題為 「臥春」 的陸游古詩 ， 要大家聽寫在筆記本上. 《 臥春 》. 暗梅幽聞花，. 臥枝傷恨底，. 遙聞臥似水，. 易透達春綠。. 岸似綠，. 岸似透綠，. 岸似透黛綠。. 國文老師朗讀如下. 有一位同學這樣寫. 《 臥春 》. 《 我蠢 》. 暗梅幽聞花，. 俺沒有文化，. 我智商很低，. 臥枝傷恨底，. 要問我是誰，. 遙聞臥似水，. 一頭大蠢驢。. 易透達春綠。. 俺是驢，. 岸似綠，. 俺是頭驢，. 岸似透綠，. 岸似透黛綠。. 俺是頭呆驢。.

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陸游古詩「臥春」之意境

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  1. 陸游古詩「臥春」之意境

  2. 鄉音濃重的國文老師，為學生們朗讀一首題為 「臥春」 的陸游古詩，要大家聽寫在筆記本上 《臥春》 暗梅幽聞花， 臥枝傷恨底， 遙聞臥似水， 易透達春綠。 岸似綠， 岸似透綠， 岸似透黛綠。

  3. 國文老師朗讀如下 有一位同學這樣寫 《臥春》 《我蠢》 暗梅幽聞花， 俺沒有文化， 我智商很低， 臥枝傷恨底， 要問我是誰， 遙聞臥似水， 一頭大蠢驢。 易透達春綠。 俺是驢， 岸似綠， 俺是頭驢， 岸似透綠， 岸似透黛綠。 俺是頭呆驢。

  4. My Homepage • Billshen.thu.edu.tw

  5. What’sEuler numbere ? From four different aspects： • Differential:1st animation2nd animation • Integral: • Limit: • Series:

  6. Overlook of Calculus • Differential Calculus and Integral Calculus • Calculus= Differential ♁ Integral ♁ FTC • Historically, Integral before Differential • Motivation: • Geometry: From slope of secant to slope of tangent • Physics:From average velocity to instantaneous velocity • Economics:From average cost to marginal cost

  7. Basic Concept on Limits • Definitions and One-sided Limits • Example 1: Power Functions • Example 2: Zero limit downstair • Example 3: Infinity limit downstair • Example 4: Limit of (Sin x)/x as x0

  8. One thing to be careful • Square root of x^2 is |x| • Example 5: Limit of √(x^2+x+1)/x as x+∞ • Example 6: Limit of √(x^2+x+1)/x as x–∞

  9. How To Calculate Limits ? • Databases: Basic and Special Limits • Limit Laws: From Known to Unknown • Sandwich Theorem: A Step Further • L’Hospital Rule: A Powerful Tool • Power Series: Back to Polyomials ?

  10. Limit Theorems

  11. Asymptotes • Horizontal Asymptotes: • Vertical Asymptotes: • Oblique Asymptotes: • Examples

  12. Algorithm on Oblique One • Assume the graph of the function f(x) has an oblique asymptote, say y=mx+b • Step 1: m=Lim (f(x)/x) as x± ∞ • Step 2: b=Lim (f(x)–mx) as x± ∞

  13. Limit Value & Fuction Value • Continuity: • Left Continuity: • Right Continuity: • Removable Discontinuity: • Unremovable Discontinuity:

  14. Finding Limits EXAMPLE For the function g(x), determine whether or not exists. If so, give the limit. SOLUTION We can see that as x gets closer and closer to 3, the values of g(x) get closer and closer to 2. This is true for values of x to both the right and the left of 3.

  15. Continuous Functions on [a,b] • Intermediate Value Theorem • Maximum-Minimum Theorem

  16. What is Rate of Change? • Change in Independent Variable  Change in Dependent Variable • Average Rate of Change = Difference Quotient = Change in Dependent V. / Change in Independent V. • Abstract Interpretation :(Average ↔ Instantaneous)Rate of Change • Geometry Interpretation:(Secant ↔ Tangent)Slope • Physics Interpretation:(Average ↔ Instantaneous) Velocity • Economics Interpretation:(Average ↔ Marginal) Cost/Revenue/Profit

  17. The Derivative as a Rate of Change

  18. What is the Derivative of f at a point? • Differentiability/Example/Non-example • Derivative ↔ Derivative Function • Geometry Interpretation:Slope of the Tangent at a point • Physics Interpretation: Instantaneous Velocity • Economics Interpretation: Marginal Cost/Revenue/Profit

  19. Compute Derivative by Definition

  20. Examples of Non-differentiability

  21. Derivative of x^α • Positive Integer: α= n • Negative Integer: α= –n • Rational #: α= n/m • Irrational #: e^(α ln(x))

  22. Differentiation Rules • Linearity Rule • Product and QuotientRules • PowerRule • ChainRule

  23. Rules of Differentiation

  24. Differentiability • Definition • Necessity：Continuity • Alternative Definition：Avoid Quotient

  25. An Easy Application • A Story of Feynman1729.03立方根~12.002 • Estimating Function Value: Approximation Formula • Linearization of a Function

  26. Derivative of Transcendental Functions • Trigonometric Functions • Exponential Functions • Logarithmic Functions • Inverse Trig Functions

  27. Derivative of Trig. Functions • Sine Function • Cosine Function • Tangent Function • Cotangent Function • Secant Function • Cosecant Function

  28. Exp & Log Functions • Derivative of Exp Functions • Derivative of Natural Exp • Derivative of Natural Log • Derivative of Log Functions

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